UKMT Senior Mathematical Challenge, 2018

For particular real numbers $a$ and $b$, the function $f$ is defined by $f(x)=ax+b$, and is such that $f(f(f(x)))=27x-52$. Which of the following formulas defines the function $g$ such that, for all values of $x$, $g(f(x))=x$?

(A) $\frac{1}{3}x-4$ (B) $\frac{1}{3}x+\frac{4}{3}$ (C) $4x-3$ (D) $\frac{1}{3}x-\frac{4}{3}$ (E) $3x-4$