Find all the values of a and b in such a way that f is continuous function on its domain.
f(x)= { (√x+a)+1 if -a ≤x ≤ 0
2x^2+3 if 0 ≤ x ≤ 1
(x+b)^2+1 if x>1
First, I think you need to include x=0 in only one branch.
f(0) = √(x+a) + 1 = 1+√a
So, we need 2x^2+3 = 1+√a at x=0
That makes a=4
Now we need f(1) to match up:
2x^2+3 = (x+b)^2+1
2+3 = (1+b)^2+1
4 = (1+b)^2
b = 1 or -3