3.21: Completed square and inverse function

Write $2x^{2} - 2x + 3$ in the form $a(x + b)^{2} + c$, where $a$, $b$ and $c$ are constants.

It is given that $f(x) = 2x^{2} - 2x + 3$ for $x \leqslant p$. Write down the greatest value of $p$ for which $f$ has an inverse.

Using this value of $p$, write down the range of $f$.

Using this value of $p$, find an expression for $f^{-1}$.