If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?

The correct option is 1/3 (x + 4).

To find the inverse function, $f^{-1}\left(x\right)$, of the given function $f\left(x\right)=3x-4$, we can follow these step-by-step logical mathematical derivations:

Step 1: Write the function as an equation in terms of y and x.
Let $y=f\left(x\right)$. This gives us the equation:
$y=3x-4$

Step 2: Solve the equation for x in terms of y.
To isolate the variable $x$, we first add $4$ to both sides of the equation:
$y+4=3x$
Next, we divide both sides of the equation by $3$ to solve for $x$:
$x=\frac{y+4}{3}$
This can also be written as:
$x=\frac{1}{3}(y+4)$

Step 3: Interchange the variables x and y to write the final inverse function.
By replacing $x$ with $f^{-1}\left(x\right)$ and $y$ with $x$, we obtain:
$f^{-1}\left(x\right)=\frac{1}{3}(x+4)$

Therefore, the inverse function $f^{-1}\left(x\right)$ is $\frac{1}{3}(x+4)$, which matches the correct option.