Problem

The function $f$ is defined by $f(x) = 2 - \frac{5}{x + 2}$ for $x > -2$.

(a) State the range of $f$.

(b) Obtain an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$.

The function $g$ is defined by $g(x) = x + 3$ for $x > 0$.

(c) Obtain an expression for $fg(x)$ giving your answer in the form $\frac{ax + b}{cx + d}$, where $a$, $b$, $c$ and $d$ are integers.