Question

Let $f\left(x\right)=3x^2-5$ and $g\left(x\right)=\frac{x}{x^2+1}$. Then find $\left(gof\right)\left(x\right)$.

Answer 1

Given, $f\left(x\right)=3x^2-5$ and $g\left(x\right)=\frac{x}{x^2+1}$.

Now,

$\left(gof\right)\left(x\right)$

$=g\left(f\right(x\left)\right)$

$=g(3x^2-5)$

$=\frac{3x^2-5}{(3x^2-5{)}^2+1}$

$=\frac{3x^2-5}{9x^4-30x^2+26}$.