Mathematics 9709 · AS & A Level · Functions

Functions — practice question

(i)[3]

Express $9x^2 - 6x + 6$ in the form $(ax + b)^2 + c$, where $a$, $b$ and $c$ are constants.

(ii)[1]

The function $f$ is defined by $f(x) = 9x^2 - 6x + 6$ for $x \geq p$, where $p$ is a constant. State the least value of $p$ that makes $f$ a one-one function.

(iii)[4]

For this value of $p$, obtain an expression for $f^{-1}(x)$, and state the domain of $f^{-1}$.

(iv)[1]

State the set of $q$ values for which the equation $f(x) = q$ has no solution.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Complete the square to obtain $(3x-1)^2+5$

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