Senior Mathematical Challenge 2018 Q23

For particular real numbers $a$ and $b$, the function $f$ is defined by $f\left(x\right)=ax+b$, and is such that $f\left(f\left(f\left(x\right)\right)\right)=27x-52$.

Which of the following formulas defines the function $g$ such that, for all values of $x$, $g\left(f\left(x\right)\right)=x$?