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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

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  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

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    Damon

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