Question

20．已知f（x）=$\left\{\begin{array}{l}{-x，x＞0}\\{{x}^{2}，x＜0}\end{array}\right.$，则f[f（x）]=（　　）

• A． $\left\{\begin{array}{l}{{x}^{2}，x＞0}\\{-{x}^{2}，x＜0}\end{array}\right.$
• B． $\left\{\begin{array}{l}{-{x}^{2}，x＞0}\\{{x}^{2}，x＜0}\end{array}\right.$
• C． $\left\{\begin{array}{l}{-x，x＞0}\\{{x}^{2}，x＜0}\end{array}\right.$
• D． $\left\{\begin{array}{l}{-x，x＜0}\\{{x}^{2}，x＞0}\end{array}\right.$

Answer 1

分析 直接利用分段函数化简求解即可．

解答 解：f（x）=$\left\{\begin{array}{l}{-x，x＞0}\\{{x}^{2}，x＜0}\end{array}\right.$，
则x＞0时，f[f（x）]=f（-x）=（-x）²=x²．
x＜0时，f[f（x）]=f（x²）=-x²．
∴f[f（x）]=$\left\{\begin{array}{l}-{x}^{2}，x＞0\\{x}^{2}，x＜0\end{array}\right.$．
故选：B．

点评 本题考查分段函数的应用，函数解析式的求法，考查计算能力．