One to one functions and inverse
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It lists one to one functions:
$g={(-5,-3),(2,5),(3,-9),(8,3)}$
$h(x)= 3x-2$
And it asks to find the following:
$g^{-1} (3) =
h^{-1}(x)=
(h * h^{-1})(-5)=$
I really need help with this problem, I especially don’t get what g does. Does it multiply all the coordinates by 3? Please help
algebra-precalculus functions inverse-function
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
asked Nov 16 at 17:13
sam A
1
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up vote
0
down vote
favorite
It lists one to one functions:
$g={(-5,-3),(2,5),(3,-9),(8,3)}$
$h(x)= 3x-2$
And it asks to find the following:
$g^{-1} (3) =
h^{-1}(x)=
(h * h^{-1})(-5)=$
I really need help with this problem, I especially don’t get what g does. Does it multiply all the coordinates by 3? Please help
algebra-precalculus functions inverse-function
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
asked Nov 16 at 17:13
sam A
1
New contributor
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
It appears that $g$ is simply a set. How do you define the inverse of a set? In all likelihood, what is meant is that the coordinates that are in the set all lie on the graph of $g(x)$. What does it mean for a point to be on the graph of a function? (Think about how you get the graph for a function.)
– Clayton
Nov 16 at 17:20
1
@Clayton A function is a set (a subset of the Cartesian product of the domain and codomain satisfying certain properties).
– smcc
Nov 16 at 17:35
3
Hi and welcome to SE. Here's a hint: $g$ is a function that, like any other function, maps values to other values. However, unlike most functions, it doesn't work for all reals. Instead, it only acts on values -5, 2, 3, and 8, and it gives you -3, 5, -9, and 3 respectively.
– Todor Markov
Nov 16 at 17:38
@smcc: A function is a rule that assigns elements of one set to another set. A graph is a subset of the product between two sets. As I stated in my first comment, the ordered pairs are likely intended to mean that $g(-5)=-3$, $g(2)=5$, etc. What Todor Markov has written also agrees with this possibility.
– Clayton
Nov 16 at 17:43
@Clayton A function is usually defined formally as a special type of relation (and a relation is a subset of the Cartesian product of two sets). Formally, a function is its graph.
– smcc
Nov 16 at 19:12
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
It lists one to one functions:
$g={(-5,-3),(2,5),(3,-9),(8,3)}$
$h(x)= 3x-2$
And it asks to find the following:
$g^{-1} (3) =
h^{-1}(x)=
(h * h^{-1})(-5)=$
I really need help with this problem, I especially don’t get what g does. Does it multiply all the coordinates by 3? Please help
algebra-precalculus functions inverse-function
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
asked Nov 16 at 17:13
sam A
1
New contributor
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
It lists one to one functions:
$g={(-5,-3),(2,5),(3,-9),(8,3)}$
$h(x)= 3x-2$
And it asks to find the following:
$g^{-1} (3) =
h^{-1}(x)=
(h * h^{-1})(-5)=$
I really need help with this problem, I especially don’t get what g does. Does it multiply all the coordinates by 3? Please help
algebra-precalculus functions inverse-function
algebra-precalculus functions inverse-function
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
asked Nov 16 at 17:13
sam A
1
New contributor
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
asked Nov 16 at 17:13
sam A
1
New contributor
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
edited Nov 16 at 18:35
N. F. Taussig
42.4k93254
42.4k93254
asked Nov 16 at 17:13
sam A
1
New contributor
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 16 at 17:13
sam A
1
asked Nov 16 at 17:13
sam A
1
1
New contributor
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
sam A is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
It appears that $g$ is simply a set. How do you define the inverse of a set? In all likelihood, what is meant is that the coordinates that are in the set all lie on the graph of $g(x)$. What does it mean for a point to be on the graph of a function? (Think about how you get the graph for a function.)
– Clayton
Nov 16 at 17:20
1
@Clayton A function is a set (a subset of the Cartesian product of the domain and codomain satisfying certain properties).
– smcc
Nov 16 at 17:35
3
Hi and welcome to SE. Here's a hint: $g$ is a function that, like any other function, maps values to other values. However, unlike most functions, it doesn't work for all reals. Instead, it only acts on values -5, 2, 3, and 8, and it gives you -3, 5, -9, and 3 respectively.
– Todor Markov
Nov 16 at 17:38
@smcc: A function is a rule that assigns elements of one set to another set. A graph is a subset of the product between two sets. As I stated in my first comment, the ordered pairs are likely intended to mean that $g(-5)=-3$, $g(2)=5$, etc. What Todor Markov has written also agrees with this possibility.
– Clayton
Nov 16 at 17:43
@Clayton A function is usually defined formally as a special type of relation (and a relation is a subset of the Cartesian product of two sets). Formally, a function is its graph.
– smcc
Nov 16 at 19:12
add a comment |
It appears that $g$ is simply a set. How do you define the inverse of a set? In all likelihood, what is meant is that the coordinates that are in the set all lie on the graph of $g(x)$. What does it mean for a point to be on the graph of a function? (Think about how you get the graph for a function.)
– Clayton
Nov 16 at 17:20
1
@Clayton A function is a set (a subset of the Cartesian product of the domain and codomain satisfying certain properties).
– smcc
Nov 16 at 17:35
3
Hi and welcome to SE. Here's a hint: $g$ is a function that, like any other function, maps values to other values. However, unlike most functions, it doesn't work for all reals. Instead, it only acts on values -5, 2, 3, and 8, and it gives you -3, 5, -9, and 3 respectively.
– Todor Markov
Nov 16 at 17:38
@smcc: A function is a rule that assigns elements of one set to another set. A graph is a subset of the product between two sets. As I stated in my first comment, the ordered pairs are likely intended to mean that $g(-5)=-3$, $g(2)=5$, etc. What Todor Markov has written also agrees with this possibility.
– Clayton
Nov 16 at 17:43
@Clayton A function is usually defined formally as a special type of relation (and a relation is a subset of the Cartesian product of two sets). Formally, a function is its graph.
– smcc
Nov 16 at 19:12
It appears that $g$ is simply a set. How do you define the inverse of a set? In all likelihood, what is meant is that the coordinates that are in the set all lie on the graph of $g(x)$. What does it mean for a point to be on the graph of a function? (Think about how you get the graph for a function.)
– Clayton
Nov 16 at 17:20
It appears that $g$ is simply a set. How do you define the inverse of a set? In all likelihood, what is meant is that the coordinates that are in the set all lie on the graph of $g(x)$. What does it mean for a point to be on the graph of a function? (Think about how you get the graph for a function.)
– Clayton
Nov 16 at 17:20
1
1
@Clayton A function is a set (a subset of the Cartesian product of the domain and codomain satisfying certain properties).
– smcc
Nov 16 at 17:35
@Clayton A function is a set (a subset of the Cartesian product of the domain and codomain satisfying certain properties).
– smcc
Nov 16 at 17:35
3
3
Hi and welcome to SE. Here's a hint: $g$ is a function that, like any other function, maps values to other values. However, unlike most functions, it doesn't work for all reals. Instead, it only acts on values -5, 2, 3, and 8, and it gives you -3, 5, -9, and 3 respectively.
– Todor Markov
Nov 16 at 17:38
Hi and welcome to SE. Here's a hint: $g$ is a function that, like any other function, maps values to other values. However, unlike most functions, it doesn't work for all reals. Instead, it only acts on values -5, 2, 3, and 8, and it gives you -3, 5, -9, and 3 respectively.
– Todor Markov
Nov 16 at 17:38
@smcc: A function is a rule that assigns elements of one set to another set. A graph is a subset of the product between two sets. As I stated in my first comment, the ordered pairs are likely intended to mean that $g(-5)=-3$, $g(2)=5$, etc. What Todor Markov has written also agrees with this possibility.
– Clayton
Nov 16 at 17:43
@smcc: A function is a rule that assigns elements of one set to another set. A graph is a subset of the product between two sets. As I stated in my first comment, the ordered pairs are likely intended to mean that $g(-5)=-3$, $g(2)=5$, etc. What Todor Markov has written also agrees with this possibility.
– Clayton
Nov 16 at 17:43
@Clayton A function is usually defined formally as a special type of relation (and a relation is a subset of the Cartesian product of two sets). Formally, a function is its graph.
– smcc
Nov 16 at 19:12
@Clayton A function is usually defined formally as a special type of relation (and a relation is a subset of the Cartesian product of two sets). Formally, a function is its graph.
– smcc
Nov 16 at 19:12
add a comment |
1 Answer
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The inverse of a function is an equation for which f(y)=x. That means, for every point (x,y) on the original function, there is a point (y,x) on the inverse. This means that $g(x)=g^{-1}(y)$, for any (x,y) pair on g(x). So, the value of $g^{-1}(3)$ is asking for what value of x is y equal to 3, the converse of $g(3)$, which is asking for what value of y is x equal to 3. For sets like g(x), that means looking through and finding pairs in the form (x,3). For equations like h(x), replace the x with y, and the y with x, and isolate the new y in the new equation. That equation is then the equation of the inverse. Then, you can evaluate that equation normally to find various values of $g^{-1}(x)$.
answered Nov 16 at 18:24
H Huang
144
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
The inverse of a function is an equation for which f(y)=x. That means, for every point (x,y) on the original function, there is a point (y,x) on the inverse. This means that $g(x)=g^{-1}(y)$, for any (x,y) pair on g(x). So, the value of $g^{-1}(3)$ is asking for what value of x is y equal to 3, the converse of $g(3)$, which is asking for what value of y is x equal to 3. For sets like g(x), that means looking through and finding pairs in the form (x,3). For equations like h(x), replace the x with y, and the y with x, and isolate the new y in the new equation. That equation is then the equation of the inverse. Then, you can evaluate that equation normally to find various values of $g^{-1}(x)$.
answered Nov 16 at 18:24
H Huang
144
New contributor
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
The inverse of a function is an equation for which f(y)=x. That means, for every point (x,y) on the original function, there is a point (y,x) on the inverse. This means that $g(x)=g^{-1}(y)$, for any (x,y) pair on g(x). So, the value of $g^{-1}(3)$ is asking for what value of x is y equal to 3, the converse of $g(3)$, which is asking for what value of y is x equal to 3. For sets like g(x), that means looking through and finding pairs in the form (x,3). For equations like h(x), replace the x with y, and the y with x, and isolate the new y in the new equation. That equation is then the equation of the inverse. Then, you can evaluate that equation normally to find various values of $g^{-1}(x)$.
answered Nov 16 at 18:24
H Huang
144
New contributor
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
up vote
0
down vote
The inverse of a function is an equation for which f(y)=x. That means, for every point (x,y) on the original function, there is a point (y,x) on the inverse. This means that $g(x)=g^{-1}(y)$, for any (x,y) pair on g(x). So, the value of $g^{-1}(3)$ is asking for what value of x is y equal to 3, the converse of $g(3)$, which is asking for what value of y is x equal to 3. For sets like g(x), that means looking through and finding pairs in the form (x,3). For equations like h(x), replace the x with y, and the y with x, and isolate the new y in the new equation. That equation is then the equation of the inverse. Then, you can evaluate that equation normally to find various values of $g^{-1}(x)$.
answered Nov 16 at 18:24
H Huang
144
New contributor
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The inverse of a function is an equation for which f(y)=x. That means, for every point (x,y) on the original function, there is a point (y,x) on the inverse. This means that $g(x)=g^{-1}(y)$, for any (x,y) pair on g(x). So, the value of $g^{-1}(3)$ is asking for what value of x is y equal to 3, the converse of $g(3)$, which is asking for what value of y is x equal to 3. For sets like g(x), that means looking through and finding pairs in the form (x,3). For equations like h(x), replace the x with y, and the y with x, and isolate the new y in the new equation. That equation is then the equation of the inverse. Then, you can evaluate that equation normally to find various values of $g^{-1}(x)$.
answered Nov 16 at 18:24
H Huang
144
New contributor
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Nov 16 at 18:24
H Huang
144
New contributor
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Nov 16 at 18:24
H Huang
144
answered Nov 16 at 18:24
H Huang
144
144
New contributor
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
H Huang is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
sam A is a new contributor. Be nice, and check out our Code of Conduct.
sam A is a new contributor. Be nice, and check out our Code of Conduct.
sam A is a new contributor. Be nice, and check out our Code of Conduct.
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It appears that $g$ is simply a set. How do you define the inverse of a set? In all likelihood, what is meant is that the coordinates that are in the set all lie on the graph of $g(x)$. What does it mean for a point to be on the graph of a function? (Think about how you get the graph for a function.)
– Clayton
Nov 16 at 17:20
1
@Clayton A function is a set (a subset of the Cartesian product of the domain and codomain satisfying certain properties).
– smcc
Nov 16 at 17:35
3
Hi and welcome to SE. Here's a hint: $g$ is a function that, like any other function, maps values to other values. However, unlike most functions, it doesn't work for all reals. Instead, it only acts on values -5, 2, 3, and 8, and it gives you -3, 5, -9, and 3 respectively.
– Todor Markov
Nov 16 at 17:38
@smcc: A function is a rule that assigns elements of one set to another set. A graph is a subset of the product between two sets. As I stated in my first comment, the ordered pairs are likely intended to mean that $g(-5)=-3$, $g(2)=5$, etc. What Todor Markov has written also agrees with this possibility.
– Clayton
Nov 16 at 17:43
@Clayton A function is usually defined formally as a special type of relation (and a relation is a subset of the Cartesian product of two sets). Formally, a function is its graph.
– smcc
Nov 16 at 19:12