Consider the following function,
f ( x ) = { e x x ≤ 0 a x + b 0 < x < 1 − x 2 + x x ≥ 1. {\displaystyle f(x)={\begin{cases}e^{x}&x\leq 0\\ax+b&0<x<1\\-x^{2}+x&x\geq 1.\end{cases}}}
where a {\displaystyle a} and b {\displaystyle b} are constants.
(a) Find values of a {\displaystyle a} and b {\displaystyle b} for which f {\displaystyle f} is continuous everywhere.
