Question

$\text{If}f\left(x\right)=x^2-1,\text{and}g\left(x\right)=x-2,$ $\text{then find a, if}gof\left(a\right)=1.$ [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)
$\text{Given,}gof\left(a\right)=1$
$\therefore a^2-3=1\Rightarrow a^2=4\Rightarrow a=\pm 2$ (1 mark)