Math Domain !!!

Calculus Level 2

A function \(f (x)\) is defined as :- \[f(x) \begin{cases} \displaystyle = x+a ,&& x<0 \\ \displaystyle = x , & \text {for} & 0 \leq{x}<1, \\ \displaystyle = b-x ,&& x \geq{1} \end{cases} \] is continuous on it's domain.

Find \(a+b\)

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