8

8. [Maximum mark: 14]
   The function $f$ is defined as $f(x)=\log_{2}(4x)$, where $x>0$.

(a) Find the value of
(i) $f(8)$;

(ii) $f\!\left(\tfrac{1}{4}\right)$. [3]

(b) Find an expression for $f^{-1}(x)$. [4]

(c) Hence, or otherwise, find $f^{-1}(0)$. [1]

The graph of $y = f(16x^{3})$ can be obtained by translating and stretching the graph of $y = \log_{2}x$.

(d) Describe these two transformations specifying the order in which they are to be applied. [6]