Cho hai hàm số f ( x ) = { 2 − x khi x < 1 x ^2 + x k h i x ≥ 1 và g ( x ) = { 2 x − x^ 2 k h i x < 1 − x^ 2 + a k h i x ≥ 1 Tìm giá trị của tham số a sao cho hàm số h ( x ) = f ( x )

\(h(x) = f(x) + g(x) = \left\{ {\begin{array}{*{20}{l}}{2 + x - {x^2}}&{{\rm{ khi }}x < 1}\\{x + a}&{{\rm{ khi }}x \ge 1}\end{array}} \right.\)

\(\begin{array}{l}\mathop {\lim }\limits_{x \to {1^ - }} h(x) = \mathop {\lim }\limits_{x \to {1^ - }} \left( {2 + x - {x^2}} \right) = \mathop {\lim }\limits_{x \to {1^ - }} 2 + \mathop {\lim }\limits_{x \to {1^ - }} x - \mathop {\lim }\limits_{x \to {1^ - }} {x^2} = 2 + 1 - {1^2} = 2;\\\mathop {\lim }\limits_{x \to {1^ + }} h(x) = \mathop {\lim }\limits_{x \to {1^ + }} (x + a) = \mathop {\lim }\limits_{x \to {1^ + }} x + \mathop {\lim }\limits_{x \to {1^ + }} a = 1 + a;h(1) = 1 + a.\end{array}\)