Mathematics

Problem

A function

g

is defined by

\begin{cases} g(x)=\sin x, & x<0,\\ g(x)=ax+b, & 0\le x<3,\\ g(x)=2x-b, & x\ge 3. \end{cases}

Determine the constants

a

and

b

so that

g

is continuous on

(-\infty,\infty)