Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=\frac{1}{3} x+9$
A) $f^{-1}(x)=3 x+27$
B) $f^{-1}(x)=\frac{1}{9} x+3$
C) $\mathrm{f}^{-1}(\mathrm{x})=\frac{1}{3} \mathrm{x}-9$
D) $\mathrm{f}^{-1}(\mathrm{x})=3 \mathrm{x}-27$

Question

Quizplus · Accepted Answer

To find the inverse function of $f(x)=\frac{1}{3}x+9$, you swap $x$ and $y$ and solve for $y$. So, $x=\frac{1}{3}y+9$. Solving for $y$ gives $y=3x-27$, which matches option D.

Determine Whether the Functions f(x)f(x)f(x) And g(x)g(x)g(x) Are Inverse Functions f(x)=13x+9f(x)=\frac{1}{3} x+9f(x)=31​x+9 A) f−1(x)=3x+27f^{-1}(x)=3 x+27f−1(x)=3x+27

Determine Whether the Functions $f(x)$ And $g(x)$ Are Inverse Functions $f(x)=\frac{1}{3} x+9$ A) $f^{-1}(x)=3 x+27$