Question

$\text{If}f\left(x\right)=9-x^2,\text{and}g\left(x\right)=x,$ $\text{then find p, if}gof\left(p\right)=0.$

Answer 1

$gof\left(p\right)=g\left\{f\right(p\left)\right\}$
$\text{Given,}f\left(x\right)=9-x^2,\text{and}g\left(x\right)=x$
$\therefore g\left\{f\right(p\left)\right\}=g\{9-p^2\}$
$=(9-p^2$) (1 mark)
$\text{Given,}gof\left(p\right)=0$
$\therefore 9-p^2=0\Rightarrow p^2=9\Rightarrow p=\pm 3$ (2 marks)