SOLUTION: I am working with Inverse functions and need help find (f(g))(x) and (g(f))(x) given f(x)=log(2)x g(x)=2 to x power sorry if that is written confusing.. on paper the 2 after log i

Question 145524: I am working with Inverse functions and need help find (f(g))(x) and (g(f))(x) given f(x)=log(2)x g(x)=2 to x power
sorry if that is written confusing.. on paper the 2 after log is lowered
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's evaluate f(g(x))

Start with the first function

Plug in

Rewrite the right side using the identity

Take the log base 2 of 2 to get 1. Note:

Multiply

------------------------

Let's evaluate g(f(x))

Start with the second function

Plug in

Let . So this means that by use of the property ====>

Replace with "y"

Now replace with "x"

So both f(g(x)) and g(f(x)) equal x.
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