A restricted parabola and its inverse

The function $f$ is defined by $f:x\mapsto(x-4)^2+1$ for $x\in\mathbb R$, $x>4$.

(i) Sketch the graph of $y=f(x)$. Your sketch should indicate the position of the graph in relation to the origin.

(ii) Find $f^{-1}(x)$, stating the domain of $f^{-1}$.

(iii) On the same diagram as in part (i), sketch the graph of $y=f^{-1}(x)$.

(iv) Write down the equation of the line in which the graph of $y=f(x)$ must be reflected in order to obtain the graph of $y=f^{-1}(x)$, and hence find the exact solution of the equation $f(x)=f^{-1}(x)$.