Question

The inverse of the function $f\left(x\right)=\frac{3x-4}{6}$ is

• A. $\frac{6x-4}{3}$
• B. $\frac{6x+3}{4}$
• C. $\frac{6x+4}{3}$
• D. $f$ is not invertible

Answer 1

The correct option is C $\frac{6x+4}{3}$

$\text{Let}y=f\left(x\right)$
$\text{Then}y=\frac{3x-4}{6}$
$\Rightarrow x=\frac{6y+4}{3}$
$\Rightarrow f^{-1}\left(y\right)=\frac{6y+4}{3}$
$\Rightarrow f^{-1}\left(x\right)=\frac{6x+4}{3}$