Use the definition of inverses to determine whether f and g are inverses.
-$f ( x ) = 3 x + 9 , \quad g ( x ) = \frac { 1 } { 3 } x - 3$
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if $f$ and $g$ are inverses, we check if $f(g(x)) = x$ and $g(f(x)) = x$. For $f(g(x))$, substitute $g(x)$ into $f$: $f(g(x)) = f\left(\frac{1}{3}x - 3\right) = 3\left(\frac{1}{3}x - 3\right) + 9 = x - 9 + 9 = x$. For $g(f(x))$, substitute $f(x)$ into $g$: $g(f(x)) = g(3x + 9) = \frac{1}{3}(3x + 9) - 3 = x + 3 - 3 = x$. Since both compositions return $x$, $f$ and $g$ are inverses.

Use the Definition of Inverses to Determine Whether F and G