Mathematics - Functions Question with Solution | TestHub

$2f\left(x^2\right)+3f\left(\frac{1}{x^2}\right)=x^2-1\Rightarrow 4f\left(x^2\right)+6f\left(\frac{1}{x^2}\right)=2x^2-2$ ..........(1)$2f\left(\frac{1}{x^2}\right)+3f\left(x^2\right)=\frac{1}{x^2}-1\Rightarrow 9f\left(x^2\right)+6f\left(\frac{1}{x^2}\right)=\frac{3}{x^2}-3$ ............(2)

(2) $-(1)\Rightarrow 5f\left(x^2\right)=\frac{3}{x^2}-2x^2-1\Rightarrow f\left(x^2\right)=\frac{3-2x^4-x^2}{5x^2}$