Mathematics

Problem

A piecewise function is defined by

f(x)=\begin{cases} mx+4, & x<-1,\\ x^{2}, & -1\le x\le 3,\\ bx-5, & x>3. \end{cases}

Determine the values of

m

and

b

that make

f

continuous at both

x=-1

and

x=3