Question

Solve for the constants a and b that make the piecewise function continuous for all real numbers. f(x)= 4-2x-x^2, x<-1 ax+b, -1 ≤x ≤1 x^3, x>1

Answer 1

when x = -1
4 - 2 x - x^2 = a x + b
4 +2 -1 = -a + b
5 = -a + b
then when x= +1
a x + b = x^3
a + b = 1
so
two equations
a + b = 1
-a + b = 5
------------------- add them
2 b = 6
b =3
a = -2