Let the function f. g. h are defined from the set of real numbers R to R such that…

Let the function \(\text { f. g. h }\) are defined from the set of real numbers R to R such that

\(f(x)=x^{2}-1\)

\(g(x)\)\(=\)  \(\sqrt{\left(x^{2}+1\right)}\)

and \(h[\mathbf{x}]\) = \(\left\{\begin{array}{llll} 0, & \text { if } & \mathbf{x}<0 \\ \mathbf{x}_{1} & \text { if } & \mathbf{x} \geqslant & \mathbf{0}^{\prime} \end{array}\right.\)then  \(\text { ho (fog) (x) }\) is defined by