the functions f and g are shown. are the functions inverses? use the drop - down menus to explain.\n\n$f(x)=x…
the functions f and g are shown. are the functions inverses? use the drop - down menus to explain.\n\n$f(x)=x - 1$\n$g(x)=x + 1$\n\nclick the arrows to choose an answer from each menu.\nthe function f(g(x)) is equal to choose...\nthe function g(f(x)) is equal to choose...\nthe functions f(x) and g(x) choose... inverses.
Answer
Explanation:
Step1: Find $f(g(x))$
Substitute $g(x)=x + 1$ into $f(x)$. So $f(g(x))=f(x + 1)=(x + 1)-1=x$.
Step2: Find $g(f(x))$
Substitute $f(x)=x - 1$ into $g(x)$. So $g(f(x))=g(x - 1)=(x - 1)+1=x$.
Step3: Determine if they are inverses
If $f(g(x))=x$ and $g(f(x))=x$, then $f(x)$ and $g(x)$ are inverse - functions.
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.