find values for a and b so that the function is continuous for all x.

Question

given g(x)=

x³-2x+2 if x≤ -2

x² +ax +b if -2<x<1

4x⁴-3x³ -5x +2 if 1≤  x

Answer 1

At x= -2 -8+4+2 = 4-2a+b or 2a-b =6 at x=1 1+a+b = 4+3-5+2 or a+ b =3. Add the two equations to get 3a= 9 or a = 3 and b = 0.