Let f(x) = .find the function so that (fog)(x)=(gof)(x)=x

Recall that if you compose a function to its inverse function, the result will be an identity function. An identity function is just a function where if you input a value, it's just going to ouput that same value. So basically it's just .

We are asked to solve for where , and . Notice that is just an identity function and a composite of and . So, it must be and must be inverses of each other ().

Please refer to my Answer from this Question to know more about Inverse Functions:

Please refer to my Answer from this Question to know the needed logarithmic properties to solve:

Recall:

Let so that the inverse of will be

. Since , we can write it as as well.

figure c

step-by-step explanation:

hope this .