Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=9 x+72, g(x)=\frac{1}{9} x-8$

Question

Quizplus · Accepted Answer

To determine if $f(x)$ and $g(x)$ are inverse functions, we can check if $f(g(x)) = x$ and $g(f(x)) = x$. Substituting $g(x)$ into $f(x)$, we get $f(g(x)) = 9(\frac{1}{9}x - 8) + 72 = x - 72 + 72 = x$. Substituting $f(x)$ into $g(x)$, we get $g(f(x)) = \frac{1}{9}(9x + 72) - 8 = x + 8 - 8 = x$. Since both compositions result in $x$, $f(x)$ and $g(x)$ are indeed inverse functions.

Determine Whether the Functions f(x)f(x)f(x) And g(x)g(x)g(x) Are Inverse Functions f(x)=9x+72,g(x)=19x−8f(x)=9 x+72, g(x)=\frac{1}{9} x-8f(x)=9x+72,g(x)=91​x−8

Determine Whether the Functions $f(x)$ And $g(x)$ Are Inverse Functions $f(x)=9 x+72, g(x)=\frac{1}{9} x-8$