Question

Base on definition of the inverse, f(g(x))=x and vice versa. Given f(x)=1/2x+3 and g(x)=2x-6, write a composition (s) should be used to prove that f(x) and g(x) are inverses of each other.

Answer 1

To verifiy if these are inverses we need to calculate the expression "f(g(x))" which uses the expression for "g(x)" in place of x on the expression of "f(x)". We have:

$\begin{gathered} f(g(x))=\frac{1}{2}(2x-6)+3 \\ f(g(x))=\frac{2x}{2}-\frac{6}{2}+3 \\ f(g(x))=x-3+3 \\ f(g(x))=x \end{gathered}$

Since the result is f(g(x)) = x, they are inverses of each other.