Restrict a quadratic and sketch its inverse

The function f is defined as $f:x\mapsto-x^2-x+6$, $x\in\mathbb R$.

(i) Explain why $f^{-1}$ does not exist.1 mark

The function f has an inverse if its domain is restricted to $x<k$.

(ii) Find the largest value of k and hence find $f^{-1}$ in a similar form.4 marks

(iii) Sketch, on the same diagram, the graphs of $f$, $f^{-1}$ and $ff^{-1}$.3 marks

(iv) Hence, solve the equation $f(x)=f^{-1}(x)$, leaving your answer in exact form.2 marks