Question

14．已知函數(shù)f（x）=$\left\{{\begin{array}{l}{sin\frac{5πx}{2}，x≤0}\\{\frac{1}{6}-{{log}_3}x，x＞0}\end{array}}$，則$f[{f（{3\sqrt{3}}）}]$=$\frac{\sqrt{3}}{2}$．

Answer 1

分析 利用分段函數(shù)逐步求解函數(shù)值即可．

解答 解：函數(shù)f（x）=$\left\{{\begin{array}{l}{sin\frac{5πx}{2}，x≤0}\\{\frac{1}{6}-{{log}_3}x，x＞0}\end{array}}$，則$f[{f（{3\sqrt{3}}）}]$=f[$\frac{1}{6}$$-lo{g}_{3}3\sqrt{3}$]=f（$-\frac{4}{3}$）=sin（$\frac{5π}{2}×（-\frac{4}{3}）$）=sin$\frac{2π}{3}$=$\frac{\sqrt{3}}{2}$．
故答案為：$\frac{{\sqrt{3}}}{2}$．

點(diǎn)評(píng) 本題考查分段函數(shù)的應(yīng)用，函數(shù)值的求法，對(duì)數(shù)運(yùn)算法則以及三角函數(shù)化簡(jiǎn)求值，考查計(jì)算能力．