Use a restricted quadratic, reflection and a fixed-point condition

The function $f$ is defined by $f:x\mapsto(ax+b)^2$, $x\in\mathbb R$, $x\geq-\dfrac ba$ where $a$ and $b$ are positive constants.

(i) Show that $f^{-1}$ exists.2 marks

(ii) State the geometrical relationship between the graphs of $f$ and $f^{-1}$. Given that the graphs of $f$ and $f^{-1}$ intersect, show that $a\leq\dfrac1{4b}$.4 marks

(iii) Show that the composite function $ff$ is defined.2 marks

(iv) Solve the equation $ff(2)=b^2$.3 marks