show that f(x)=.25*in(x) and g(x)=e^(4x) are inverse functions.

Question

anonymous · Answer

Hint: if they are to be inverse, they must satisfy the property $f(g(x))=g(f(x))=x$.  Show that that equality holds for all $x$.

kropot72 · Answer

$$Let\ f(x) = y$$
$$y=0.25\times \ln x$$
To find f(x)^-1 interchange x and y and solve for y.
$$x=0.25\times \ln y$$
$$\ln y=4x ........(1)$$
Can you solve e

anonymous · Answer

@kropot72, technically, that is not a proof, but rather a derivation, which is contrary to what the question is asking.

kropot72 · Answer

Can you solve equation (1) to find y?

anonymous · Answer

it satisfys both methods. I need a proof, so ill use the first one. thanks to both of you.

kropot72 · Answer

@yakeyglee The question does not ask for a proof but states "Show that.........".
I had intended to point out that the inverse of the second expression should also be found to show that each expression was the inverse of the other.

anonymous · Answer

@kropot72  Questions that ask "Show that..." request a proof.  Think about how you would approach these two questions differently:
-Show that $x=4$ is a solution to $x^2-3x-4=0$.
-Find a positive solution of $x^2-3x-4=0$.

The first requests a proof, the second requests a derivation.  The first one is analogous to this problem.

kropot72 · Answer

@yakeyglee You have made a good point :)