Question

17．已知函數(shù)f（x）=$\left\{\begin{array}{l}{（{\frac{1}{3}}）^x}{，_{\;}}_{\;}x≤1\\{log_{\frac{1}{2}}}x{，_{\;}}x＞1\end{array}\right.$，則f（f（${\sqrt{2}}$））=（　�。�

• A． $-\frac{1}{2}$
• B． $\frac{1}{2}$
• C． $\sqrt{3}$
• D． $\frac{{\sqrt{3}}}{3}$

Answer 1

分析 由已知中函數(shù)f（x）=$\left\{\begin{array}{l}{（{\frac{1}{3}}）^x}{，_{\;}}_{\;}x≤1\\{log_{\frac{1}{2}}}x{，_{\;}}x＞1\end{array}\right.$，將x=$\sqrt{2}$代入可得答案．

解答 解：∵函數(shù)f（x）=$\left\{\begin{array}{l}{（{\frac{1}{3}}）^x}{，_{\;}}_{\;}x≤1\\{log_{\frac{1}{2}}}x{，_{\;}}x＞1\end{array}\right.$，
∴f（${\sqrt{2}}$）=$-\frac{1}{2}$　　
f（f（${\sqrt{2}}$））=f（$-\frac{1}{2}$）=$\sqrt{3}$，
故選：C．

點(diǎn)評(píng) 本題考查的知識(shí)點(diǎn)是分段函數(shù)的應(yīng)用，函數(shù)求值，指數(shù)和對(duì)數(shù)的運(yùn)算性質(zhì)，難度中檔．