Functions $$$\mathrm{f}$$$ and $$$\mathrm{g}$$$ are defined as follows: $$\[ \begin{aligned} &\mathrm{f}: x \mapsto x^{2}+2 x+3 \text { for } x \leqslant-1, \\ &\mathrm{~g}: x \mapsto 2 x+1 \text { for } x \geqslant-1 \end{aligned} \]$$ Solve the equation $$$\operatorname{gf}(x)=13$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_12 Year：2021 Question No：7(c)

Answer:

$
2\left(x^{2}+2 x+3\right)+1=13
$
$2 x^{2}+4 x-6[=0]$ leading to $(2)(x-1)(x+3)[=0]$
$
x=-3 \text { only }
$

1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)

1.2.2 identify the range of a given function in simple cases, and find the composition of two given functions