Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The functions $f$ and $g$ are given by $f(x) = \cos x$ for $0 \leq x \leq \pi$, and by $g(x) = 3\cos(x - \pi) + 2$ for $\pi \leq x \leq 2\pi$.

(a)[4]

Give a complete description of the transformations combined to change the graph of $y = f(x)$ into the graph of $y = g(x)$.

(b)[4]

Using the axes provided, sketch the graphs of $y = f(x)$ and $y = g(x)$.

(c)[4]

Find $g^{-1}\!\left(f\!\left(\frac{1}{3}\pi\right)\right)$.

(d)[1]

Explain why the composite function $fg$ cannot be formed.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Identifies stretch factor $3$ in $y$-direction” …