Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=6 x+42, g(x)=\frac{1}{6}(x-42)$

Question

Quizplus · Accepted Answer

To verify 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 $f(g(x)) = 6\left(\frac{1}{6}(x-42)\right) + 42 = x$. Substituting $f(x)$ into $g(x)$, we get $g(f(x)) = \frac{1}{6}((6x+42)-42) = x$. Since both conditions are satisfied, $f(x)$ 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)=6x+42,g(x)=16(x−42)f(x)=6 x+42, g(x)=\frac{1}{6}(x-42)f(x)=6x+42,g(x)=61​(x−42)

Determine Whether the Functions $f(x)$ And $g(x)$ Are Inverse Functions $f(x)=6 x+42, g(x)=\frac{1}{6}(x-42)$