Question

Let $f:R\to R$ be a function whose inverse is $\frac{x+5}{3}$. What is $f\left(x\right)$ equal to?

• A. $f\left(x\right)=3x+5$
• B. $f\left(x\right)=3x-5$
• C. $f\left(x\right)=5x-3$
• D. $f\left(x\right)$ does not exist

Answer 1

The correct option is B $f\left(x\right)=3x-5$

Given : $f^{-1}\left(x\right)=\frac{x+5}{3}$

Let $y=f^{-1}\left(x\right)$

$\Rightarrow y=\frac{x+5}{3}$

$\Rightarrow x=3y-5\Rightarrow f\left(y\right)=3y-5\Rightarrow f\left(x\right)=3x-5$
Option B is correct.