Mathematics - Functions Question with Solution | TestHub

Put $g(x)=y=x^2-2\Rightarrow x=\sqrt{y+2}\Rightarrow f(\sqrt{y+2})=0$

$$\Rightarrow y^5+20y^4+40y^3+79y^2+74y+23=0$$

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

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

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

$$\therefore g(x_1)\cdot g(x_2)\cdot g(x_3)\cdot g(x_4)\cdot g(x_5)-30g(x_1{x}_2{x}_3{x}_4{x}_5)=-23+30=7$$