(a) It is given that

\(f:x\mapsto\sqrt{x}\quad\text{for }x\geq0,\)

\(g:x\mapsto x+5\quad\text{for }x\geq0.\)

Identify each of the following functions with one of \(f^{-1}\), \(g^{-1}\), \(fg\), \(gf\), \(f^2\), \(g^2\).

(i) \(\sqrt{x+5}\)

(ii) \(x-5\)

(iii) \(x^2\)

(iv) \(x+10\)

(b) It is given that

\(h(x)=a+\frac{b}{x^2},\)

where \(a\) and \(b\) are constants.

(i) Why is \(-2\leq x\leq2\) not a suitable domain for \(h(x)\)?

(ii) Given that \(h(1)=4\) and \(h'(1)=16\), find the value of \(a\) and of \(b\).