Inverse functions

[jess5085]

Hello,For this question:f(x) = e^2x and g(x) = 3/2 In(x)Find (fog) (x) and hence solve (fog)(x) = 3I got up to (fog)(x) = e^3In (x) and I don't know how to continueThanks in advance!

 

[Ishuda]

Hello,For this question:f(x) = e^2x and g(x) = 3/2 In(x)Find (fog) (x) and hence solve (fog)(x) = 3I got up to (fog)(x) = e^3In (x) and I don't know how to continueThanks in advance!

First I'll add some parenthesis to make more clear the functions. Hopefully I'll add them in the correct place.
f(x) = e^(2 x) = \(\displaystyle e^{2 x}\)
g(x) = (3/2) ln(x) = \(\displaystyle \frac{3}{2} ln(x)\)

I believe this is consistent with what you have
(fog)(x) = \(\displaystyle e^{3\, ln(x)}\)

You now need some of the rules of logarithms:
a log(b) = log(b^a)
and
a^log_a(b) = b
Oh and ln(x) = log_e(x)