Mathematics

Problem

Given that

c\ne 0

, determine the real numbers

c

and

d

that make the function

p(x)= \begin{cases} c x +1, & x<-2,\\ \dfrac{c}{x}, & -2\le x < 1,\\ \sqrt{x+4}+ d, & x\ge 1 \end{cases}

continuous on its domain.