Question

O GRAPHS AND FUNCTIONSDetermining whether two functions are inverses of each other

Answer 1

Recall that if functions f(x) and g(x) are inverses, their compositions will equal x.

QUESTION A

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

The compositions are calculated as follows:

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

and

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

Therefore, f and g are inverses of each other.

QUESTION B

$\begin{gathered} f(x)=-\frac{4}{x} \\ g(x)=\frac{4}{x} \end{gathered}$

The compositions are calculated as follows:

$\begin{gathered} f(g(x))=-\frac{4}{(\frac{4}{x})} \\ f(g(x))=-x \end{gathered}$

and

$\begin{gathered} g(f(x))=\frac{4}{(-\frac{4}{x})} \\ g(f(x))=-x \end{gathered}$

Therefore, f and g are not inverses of each other.