Answer to Question #237902 in Calculus for CCW

Question

Unit 1 Review:

3) Using the definition of an inverse, explain why f(x) and g(x) inverses of one another?

Why or why not?

Answer 1

They are not inverses of one another. For them to be, then $f(g(x))=g(f(x))=x$

But $f(x)=3^{2x} +1 \text{ and } g(x)=\log{(x-1)}\\ f(g(x))=x^2-2x+2\neq x\\ g(f(x))=2x\neq x\\ \text{Hence they are not inverses of one another}$