Find the value for a so there is no jump discontinuity in the function. f(x) = { (x + 3)^2 , x ≤ −2 x + a, x > −2

Question

I am not sure how solve this. The one thing I do know is that I have to set both (x+3)^2 and x+a equal to the same thing. I am just not sure what to set the functions equal too. The answer is a=3.

Answer 1

We just set the value of the two functions to be equal at x = -2

(x+3)^2 = (-2 + 3)^2 = 1^2 = 1

x + a = -2 + a

1 = -2 + a

3 = a