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: Find \( f(g(x)) \)

Substitute \( g(x)=x + 1 \) into \( f(x) \).
\( f(g(x))=f(x + 1)=(x + 1)-1=x \)

Step2: Find \( g(f(x)) \)

Substitute \( f(x)=x - 1 \) into \( g(x) \).
\( g(f(x))=g(x - 1)=(x - 1)+1=x \)

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.