Question

$\text{If}f\left(x\right)=x^2-1,\text{and}g\left(x\right)=x-2,$ $\text{then find a, if}gof\left(a\right)=6.$ [2 marks]

Answer 1

$gof\left(a\right)=g\left\{f\right(a\left)\right\}$
$\text{Given,}f\left(x\right)=x^2-1,\text{and}g\left(x\right)=x-2$
$\therefore g\left\{f\right(a\left)\right\}=g\{a^2-1\}$
$=(a^2-1)-2=a^2-3$ [1 mark]
$\text{Given,}gof\left(a\right)=6$
$\therefore a^2-3=6\Rightarrow a^2=9\Rightarrow a=\pm 3$ [1 mark]