Use composition of functions to prove that $f(x) =e^x-e^{-x}$ and $g(x) = lnleft(frac {x+sqrt{x^2 +...
I have found no way of composing these two functions
$$f(x) =e^x-e^{-x} quad g(x) = lnleft(frac {x+sqrt{x^2 + 4}}{2}right)$$
that has proven these two are inverses.
If there is anyone that can help, that would be appreciated
calculus functions logarithms
edited Nov 26 at 17:36
gimusi
1
asked Nov 26 at 17:28
Hector Espinoza
194
closed as off-topic by José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs Nov 27 at 9:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
I have found no way of composing these two functions
$$f(x) =e^x-e^{-x} quad g(x) = lnleft(frac {x+sqrt{x^2 + 4}}{2}right)$$
that has proven these two are inverses.
If there is anyone that can help, that would be appreciated
calculus functions logarithms
edited Nov 26 at 17:36
gimusi
1
asked Nov 26 at 17:28
Hector Espinoza
194
closed as off-topic by José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs Nov 27 at 9:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
I have found no way of composing these two functions
$$f(x) =e^x-e^{-x} quad g(x) = lnleft(frac {x+sqrt{x^2 + 4}}{2}right)$$
that has proven these two are inverses.
If there is anyone that can help, that would be appreciated
calculus functions logarithms
edited Nov 26 at 17:36
gimusi
1
asked Nov 26 at 17:28
Hector Espinoza
194
I have found no way of composing these two functions
$$f(x) =e^x-e^{-x} quad g(x) = lnleft(frac {x+sqrt{x^2 + 4}}{2}right)$$
that has proven these two are inverses.
If there is anyone that can help, that would be appreciated
calculus functions logarithms
calculus functions logarithms
edited Nov 26 at 17:36
gimusi
1
asked Nov 26 at 17:28
Hector Espinoza
194
edited Nov 26 at 17:36
gimusi
1
asked Nov 26 at 17:28
Hector Espinoza
194
edited Nov 26 at 17:36
gimusi
1
edited Nov 26 at 17:36
gimusi
1
edited Nov 26 at 17:36
gimusi
1
1
asked Nov 26 at 17:28
Hector Espinoza
194
asked Nov 26 at 17:28
Hector Espinoza
194
asked Nov 26 at 17:28
Hector Espinoza
194
194
closed as off-topic by José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs Nov 27 at 9:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs Nov 27 at 9:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – José Carlos Santos, max_zorn, Cyclohexanol., Saad, Gibbs
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
HINT
Show that
$$f((g(x))=frac {x+sqrt{x^2 + 4}}{2}-frac 2{x+sqrt{x^2 + 4}}=x$$
and
$$g((f(x))= lnleft(frac {(e^x-e^{-x})+sqrt{(e^x-e^{-x})^2 + 4}}{2}right)=x$$
answered Nov 26 at 17:33
gimusi
1
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
HINT
Show that
$$f((g(x))=frac {x+sqrt{x^2 + 4}}{2}-frac 2{x+sqrt{x^2 + 4}}=x$$
and
$$g((f(x))= lnleft(frac {(e^x-e^{-x})+sqrt{(e^x-e^{-x})^2 + 4}}{2}right)=x$$
answered Nov 26 at 17:33
gimusi
1
add a comment |
HINT
Show that
$$f((g(x))=frac {x+sqrt{x^2 + 4}}{2}-frac 2{x+sqrt{x^2 + 4}}=x$$
and
$$g((f(x))= lnleft(frac {(e^x-e^{-x})+sqrt{(e^x-e^{-x})^2 + 4}}{2}right)=x$$
answered Nov 26 at 17:33
gimusi
1
add a comment |
HINT
Show that
$$f((g(x))=frac {x+sqrt{x^2 + 4}}{2}-frac 2{x+sqrt{x^2 + 4}}=x$$
and
$$g((f(x))= lnleft(frac {(e^x-e^{-x})+sqrt{(e^x-e^{-x})^2 + 4}}{2}right)=x$$
answered Nov 26 at 17:33
gimusi
1
HINT
Show that
$$f((g(x))=frac {x+sqrt{x^2 + 4}}{2}-frac 2{x+sqrt{x^2 + 4}}=x$$
and
$$g((f(x))= lnleft(frac {(e^x-e^{-x})+sqrt{(e^x-e^{-x})^2 + 4}}{2}right)=x$$
answered Nov 26 at 17:33
gimusi
1
edited Nov 26 at 17:55
answered Nov 26 at 17:33
gimusi
1
answered Nov 26 at 17:33
gimusi
1
answered Nov 26 at 17:33
gimusi
1
1
add a comment |
add a comment |
