Problem

(a) Express $3x^2 - 12x + 14$ in the form $3(x + a)^2 + b$, where $a$ and $b$ are constants to be found.

The function $f(x) = 3x^2 - 12x + 14$ is defined for $x \geq k$, where $k$ is a constant.

(b) Find the least value of $k$ for which the function $f^{-1}$ exists.

For the rest of this question, you should assume that $k$ has the value found in part (b).

(c) Find an expression for $f^{-1}(x)$.

(d) Hence or otherwise solve the equation $ff(x) = 29$.