Mathematics - Functions Question with Solution | TestHub

$g\left(f\left(x\right)\right)=4{\left(\frac{5}{4}\right)}^2-10.\frac{5}{4}+5=-\frac{5}{4}$
$g\left(f\left(\frac{5}{4}\right)\right)=f^2\left(\frac{5}{4}\right)+f\left(\frac{5}{4}\right)-1$
$-\frac{5}{4}=f^2\left(\frac{5}{4}\right)+f\left(\frac{5}{4}\right)-1$
$f^2\left(\frac{5}{4}\right)+f\left(\frac{5}{4}\right)+\frac{1}{4}=0$
${\left(f\left(\frac{5}{4}\right)+\frac{1}{2}\right)}^2=0$
$f\left(\frac{5}{4}\right)=-\frac{1}{2}$