analytically show that the functions are inverse functions.
f(x)=e^2x
g(x)=ln sqr rt(x)

Question

asnaseer · Answer

$$y=e^{2x}$$take logs of both sides to get:$$\ln(y)=2x$$rearrange to get:$$x=\frac{1}{2}\ln(y)=\ln(y^\frac{1}{2})=\ln(\sqrt{y})$$

asnaseer · Answer

therefore:$$g(x)=f^{-1}(x)$$

asnaseer · Answer

do you follow?

anonymous · Answer

not exactly. i mean i understand your math, i'm just confused on the whole inverse thing...

asnaseer · Answer

if f(x) is some function which returns a value for each value of 'x' you plug into it.
the inverse would mean, if you are given the value of f(x), then what value of x was used to get that.

asnaseer · Answer

so in the first part of the proof, I got:$$x=\ln(\sqrt{y})=\ln(\sqrt{f(x)})$$
what this is saying is that given a value for f(x), work out what x should be to get that value.

anonymous · Answer

so is $$f ^{-1}(x)=g(x)$$ and $$g ^{-1}(x)=f(x)$$

asnaseer · Answer

yes