Hi everyone, this is a problem from a previous exam. I manage to solve half of it, but am struggling with the second half.

f(x) = x^{2}+ x - 1 for x ≥ 0

f(x) = a cos(x) + b sin(x) for x < 0

Find a and b so that f(x) is continuous and differentiable for all x = 0

Can someone help solve this?

Thank you all!