Question: The following functions are differentiable. For each function, verify that it has inverse and find \(\left( {{f}^{-1}} \right)'\left( a \right)\)

(a) \(f\left( x \right)={{x}^{3}}+x+1,\,\,\,\,a=11\)

(b) \(f\left( x \right)=\frac{3}{{{x}^{3}}}-x,\,\,\,x<0,\,\,a=-2\)