Schultz Washington

06/11/2024 · Middle School

For each pair of functions \( f \) and \( g \) below, find \( f(g(x)) \) and \( g(f(x)) \). Then, determine whether \( f \) and \( g \) are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all \( x \) in the domain of the composition. You do not have to indicate the domain.) (a) \[ \begin{array}{l} f(x)=-\frac{6}{x}, x \neq 0 \\ g(x)=-\frac{6}{x}, x \neq 0 \\ f(g(x))= \\ g(f(x))=\square \end{array} \] (b) \[ \begin{array}{l} f(x)=x+2 \\ g(x)=-x+2 \\ f(g(x))=\square \\ g(f(x))=\square \end{array} \] \( f \) and \( g \) are inverses of each other \( f \) and \( g \) are inverses of each other \( f \) and \( g \) are not inverses of each other \( f \) and \( g \) are not inverses of each other