(a)[1]
Find an expression for $f^{-1}(x)$.
(b)[2]
The diagram shows the curve $y = g(x)$, where $g(x) = \frac{1}{x^2 + 2}$ for $x \in \mathbb{R}$. State the range of $g$ and explain whether $g^{-1}$ exists.
(c)[4]
The function $h$ is defined by $h(x) = \frac{1}{x^2 + 2}$ for $x \geq 0$. Solve the equation $hf(x) = f\left(\frac{25}{16}\right)$. Give your answer in the form $a + b\sqrt{c}$, where $a$, $b$ and $c$ are integers.