Question

Let $f:R\to R$ be defined by $f\left(x\right)=3x-4,$then $f^{-1}\left(x\right)$ is:

• A. $\frac{x+4}{3}$
• B. $\frac{x-4}{3}$
• C. $3x+4$
• D. Not defined

Answer 1

The correct option is A

$\frac{x+4}{3}$

Finding the value of $f^{-1}\left(x\right)$.

We have, $f\left(x\right)=3x-4$

In order to find $f^{-1}\left(x\right)$, we will make $x$ as the subject.

$$\begin{gathered} \text{Let}y=3x-4 \\ \Rightarrow 3x=y+4 \\ \Rightarrow x=\frac{y+4}{3} \\ \therefore f^{-1}\left(x\right)=\frac{x+4}{3} \end{gathered}$$

Therefore, the correct answer is Option (A).