Question

17．已知函數(shù)f（x）=$\left\{\begin{array}{l}{1+{4}^{x}，x≤0}\\{lo{g}_{2}x，x＞0}\end{array}\right.$，則f（f（$\frac{\sqrt{2}}{4}$））等于（　�。�

• A． $\frac{9}{8}$
• B． $\frac{5}{4}$
• C． $\frac{11}{8}$
• D． $\frac{7}{4}$

Answer 1

分析 根據(jù)函數(shù)解析式先求出f（$\frac{\sqrt{2}}{4}$）的值，再求出f（f（$\frac{\sqrt{2}}{4}$））的值．

解答 解：由題意得，f（x）=$\left\{\begin{array}{l}{1+{4}^{x}，x≤0}\\{lo{g}_{2}x，x＞0}\end{array}\right.$，
則f（$\frac{\sqrt{2}}{4}$）=${log}_{2}^{\frac{\sqrt{2}}{4}}$=${log}_{2}^{\sqrt{2}}$-${log}_{2}^{4}$=$\frac{1}{2}-$2=$-\frac{3}{2}$，
f（$-\frac{3}{2}$）=1+${4}^{-\frac{3}{2}}$=1+$\frac{1}{8}$=$\frac{9}{8}$，
所以f（f（$\frac{\sqrt{2}}{4}$））=$\frac{9}{8}$，
故選：A．

點(diǎn)評 本題考查分段函數(shù)的多層函數(shù)值，解題時(shí)應(yīng)根據(jù)從內(nèi)到外的順序，由分段函數(shù)的解析式依次求出函數(shù)值，屬于基礎(chǔ)題．