Question

the functions f and g are shown. are the functions inverses? use the drop - down menus to explain. f(x)=x - 1 g(x)=x + 1 click the arrows to choose an answer from each menu. the function f(g(x)) is equal to choose... the function g(f(x)) is equal to choose... the functions f(x) and g(x) choose... inverses.

Explanation:

Step1: Compute $f(g(x))$

Substitute $g(x)$ into $f(x)$:
$f(g(x)) = f(x+1) = (x+1) - 1 = x$

Step2: Compute $g(f(x))$

Substitute $f(x)$ into $g(x)$:
$g(f(x)) = g(x-1) = (x-1) + 1 = x$

Step3: Determine if inverses

Two functions are inverses if $f(g(x))=x$ and $g(f(x))=x$ for all $x$ in their domains.

Answer:

The function $f(g(x))$ is equal to $x$.
The function $g(f(x))$ is equal to $x$.
The functions $f(x)$ and $g(x)$ are inverses.