Question

9．已知函數(shù)$f（x）=\left\{{\begin{array}{l}{{2^{1-x}}，x≤1}\\{1-log_2^x，x＞1}\end{array}}\right.$，則滿足f（x）≤4的x取值范圍是（　　）

• A． [-1，+∞）
• B． $[\frac{1}{8}，+∞）$
• C． $[-1，\frac{1}{8}]$
• D． $[\frac{1}{8}，1]$

Answer 1

分析 利用分段函數(shù)列出不等式組轉(zhuǎn)化求解即可．

解答 解：函數(shù)$f（x）=\left\{{\begin{array}{l}{{2^{1-x}}，x≤1}\\{1-log_2^x，x＞1}\end{array}}\right.$，則滿足f（x）≤4，
可得：$\left\{\begin{array}{l}{x≤1}\\{{2}^{1-x}≤4}\end{array}\right.$或$\left\{\begin{array}{l}{x＞1}\\{1-lo{g}_{2}x≤4}\end{array}\right.$，
解得x∈[-1，1]或x∈（1，+∞）．
函數(shù)$f（x）=\left\{{\begin{array}{l}{{2^{1-x}}，x≤1}\\{1-log_2^x，x＞1}\end{array}}\right.$，則滿足f（x）≤4的x取值范圍是：[-1，+∞）．
故選：A．

點(diǎn)評 本題考查分段函數(shù)的應(yīng)用，指數(shù)與對數(shù)不等式的解法，考查計(jì)算能力．