Question

19．已知函數(shù)$f（x）=\left\{\begin{array}{l}{x^2}-x，x≤0\\-{2^x}，x＞0\end{array}\right.$，則“f（x）≤0”是“x=0”的（　�。�條件．

• A． 充分不必要
• B． 必要不充分
• C． 充要
• D． 既不充分也不必要

Answer 1

分析 x=0⇒f（x）=0．f（x）≤0，可得$\left\{\begin{array}{l}{x≤0}\\{{x}^{2}-x≤0}\end{array}\right.$或$\left\{\begin{array}{l}{x＞0}\\{-{2}^{x}≤0}\end{array}\right.$，解得x即可判斷出結(jié)論．

解答 解：x=0⇒f（x）=0．
f（x）≤0，可得$\left\{\begin{array}{l}{x≤0}\\{{x}^{2}-x≤0}\end{array}\right.$或$\left\{\begin{array}{l}{x＞0}\\{-{2}^{x}≤0}\end{array}\right.$，
解得x=0或x＞0．
∴“f（x）≤0”是“x=0”的必要不充分條件．
故選：B．

點(diǎn)評(píng) 本題考查了分段函數(shù)的性質(zhì)、不等式的解法、簡(jiǎn)易邏輯的判定方法，考查了推理能力與計(jì)算能力，屬于基礎(chǔ)題．