Mathematics - Functions Question with Solution | TestHub

Put $g(x)=y=x^2-2\Rightarrow x=\sqrt{y+2}\Rightarrow f(\sqrt{y+2})=0$ $\Rightarrow y^5+20y^4+40y^3+79y^2+74y+23=0$

Roots are $g\left(x_1\right),g\left(x_2\right),g\left(x_3\right),g\left(x_4\right),g\left(x_5\right)$

$g\left(x_1\right)\cdot g\left(x_2\right)\cdot g\left(x_3\right)\cdot g\left(x_4\right)\cdot g\left(x_5\right)=-23$

And $x_1{x}_2{x}_3{x}_4{x}_5=-1$

$g\left(x_1{x}_2{x}_3{x}_4{x}_5\right)=g(-1)=-1$

$\therefore g\left(x_1\right)\cdot g\left(x_2\right)\cdot g\left(x_3\right)\cdot g\left(x_4\right)\cdot g\left(x_5\right)-30g\left(x_1{x}_2{x}_3{x}_4{x}_5\right)$

=-23+30=7