Use the definition of inverses to determine whether f and g are inverses.
-$f ( x ) = 5 x + 25 , \quad g ( x ) = \frac { 1 } { 5 } x - 5$

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 $f$, yielding $f\left(\frac{1}{5}x - 5\right) = 5\left(\frac{1}{5}x - 5\right) + 25 = x - 25 + 25 = x$. For $g(f(x))$, substitute $f(x)$ into $g$, yielding $g(5x + 25) = \frac{1}{5}(5x + 25) - 5 = x + 5 - 5 = x$. Since both compositions return $x$, $f$ and $g$ are inverses.

Use the Definition of Inverses to Determine Whether F and G