If $f: R→ R, g: R → R$ and $h: R →R$ be three functions given by $f(x) = x^2 -1,g(x)=\sqrt{x^2+1}$ and $h(x) =\left\{\begin{matrix}0,& x ≤ 0\\x, &x >0\end{matrix}\right.$, then the composite function $(ho\, fog) (x)$ is given by
Answer & explanation
Correct answer: option 2
We have,
$(hofog) (x) = h (fog\, (x)) = h (f (g(x)) = h(f(\sqrt{x^2 + 1}))$
$⇒(hofog) (x) = h (x^2+1-1)=h (x^2)$
$⇒(hofog) (x) =\left\{\begin{matrix}x^2,& x ≠ 0\\0, &x =0\end{matrix}\right.$