Question

If $f\left(x\right)=3x-5,then{f}^{-1}\left(x\right)$.

• A. is given by $\frac{1}{3x-5}$
• B. is given by $\frac{x+5}{3}$
• C. does not exist because f is not one-one
• D. does not exist because f is not onto

Answer 1

Answer: (B)

is given by $\frac{x+5}{3}$

Given, $f\left(x\right)=3x-5$

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

$\Rightarrow x=f\left(y\right)=3y-5$

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