Calc and vector's summer school math question

Question

Hey can anyone help me out with this math homework? We're on limits and I've been trying but I can't quite figure out how to solve it:

If,

f(x) = a^2-x^2 for {-4< x ≤ -2}

f(x) = b-x for {-2 ≤ x ≤ -1} is continuous

f(x) = x^2 a for {-1 < x ≤ 4}

Find the values of a and b

Thanks

Answer 1

For f to be continuous, the following conditions must hold.

When x = - 2:

a^2 - x^2 = b - x

a^2 - 4 = b + 2

a^2 - b = 6 ...(1)

When x = - 1:

b - x = x^2 + a

b + 1 = 1 + a

b = a ...(2)

Eliminating b from (1) and (2):

a^2 - a - 6 = 0

(a - 3)(a + 2) = 0

a = 3 or - 2.

a = b = 3 or a = b = 2.