Question

If f : R → R such that f(x) = 3x - 4 then which of the following is $f^{}\left(x\right)$ ?

1. $\frac{x+4}{3}$
2. $\frac{1}{3}x-4$
3. $3x-4$
4. $3x+5$

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

Solution :-

For finding inverse of a function we actually find which image related with whose pre-image and given that image is $f\left(x\right)=3x-4$ .

Now, let $y=3x-4\left(\text{Here}y\text{is image of}x\right)\mathrm{.}$ For finding pre-image of $y$ we have to find $x$ .

Now, we have

Hence, $f^{}\left(y\right)=\frac{y+4}{3}$ . This is the inverse of given function $f\left(x\right)$ .
Here in this equation we replace $y$ with $x$ then, we get

So, the correct answer is option-1, $\to \frac{x+4}{3}$