CAIE A-Level Mathematics AS 1.2.2 Range and Composition Questions

$\left[\operatorname{gf}\left(\frac{7}{2}\right)=\right] 2\left(\left(x+\frac{7}{2}\right)^{2}-\frac{7}{2}\right)-1$ or $2 x^{2}+4\left(\frac{7}{2}\right) x+2\left(\frac{7}{2}\right)^{2}-2\left(\frac{7}{2}\right)-1[=0]$
OE

Alternatively, $[\mathrm{gf}(x)=0 \Rightarrow] \mathrm{f}(x)=\frac{1}{2}$.

$$\begin{aligned} {[x=]-\frac{7}{2} \pm 2 \text { or } \frac{-14 \pm \sqrt{14^{2}-4 \times 2 \times \frac{33}{2}}}{4}} {\left[\frac{-14 \pm \sqrt{64}}{4}\right] \text { or factorising }} \end{aligned}$$
OE

Solving their three term quadratic equation as far as two solutions or correctly selecting the negative root only.

Alternatively, $\pm \sqrt{\frac{1}{2}+\frac{7}{2}}-\frac{7}{2}$.

$[x=]-\frac{11}{2}$
If B1M0 scored then award SCB1 for the correct final answer.