Question Number 38535 by Rio Mike last updated on 27/Jun/18
$${Given}\:{the}\:{function} \\ $$$${f}\left({x}\right)\:{where}\: \\ $$$$ \\ $$$${f}\left({x}\right)=\:\begin{cases}{\int{x}^{\mathrm{2}} \:+\:\mathrm{1}\:,{for}\:\left\{{x}:{x}\:{D}\left({f}\right)\:\mathrm{2}\right.}\\{\int{x}^{\mathrm{3}} \:−\:\mathrm{1},{for}\:{y}\:=\:{f}'\left({x}\right)}\end{cases} \\ $$$$\left.{a}\right)\:{Evaluate}\:{f}\left(\mathrm{2}\right) \\ $$$${if}\:{f}\left({a}\right)=\:\mathrm{2}\:+\:{a}^{{n}−\mathrm{1}} \\ $$$${find}\:{the}\:{value}\:{of}\:{a} \\ $$$${hence}\:{the}\:{domain}\:{of}\:{f}\left({x}\right). \\ $$