Let \(f:\mathbb{R}\rightarrow \mathbb{R}\) defined by \(f(x)=3x^2-5\) and \(g:\mathbb{R}\rightarrow\mathbb{R}\) by \(g(x)=\frac{x}{x^2+1}\) then \(g\circ f\) is

\(\frac{3x^2-5}{9x^4-30x^2+26}\)

\((g\circ f)x=g(f(x))\)

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

= \(\frac{3x^2 - 5}{9x^4 + 25 - 30x^2 + 1 }\)

= \(\frac{3x^2-5}{9x^4-30x^2+26}\)