Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The function $f : x \mapsto x^2 - 4x + k$ is given on the domain $x \geq p$, with $k$ and $p$ as constants.
(i)[2]

Write $f(x)$ in the form $(x + a)^2 + b + k$, where $a$ and $b$ are constants.

(ii)[1]

State the range of $f$ in terms of $k$.

(iii)[1]

State the smallest value of $p$ for which $f$ is one-one.

(iv)[4]

Using the value of $p$ obtained in part (iii), determine an expression for $f^{-1}(x)$ and state the domain of $f^{-1}$, with both answers written in terms of $k$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Complete the square to obtain $(x-2)^2 -4 + k$.

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