Question

若函數(shù)y=（log_0.5a）^x在R上為增函數(shù)，則a的取值范圍是    ．

Answer 1

【答案】分析：利用指數(shù)函數(shù)的單調(diào)性，底數(shù)log_0.5a＞1，解此不等式即可．
解答：解：根據(jù)指數(shù)函數(shù)的單調(diào)性，可知底數(shù)log_0.5a＞1，即log_0.5a＞log_0.5^0.5，
根據(jù)對數(shù)函數(shù)的單調(diào)性，∴0＜a＜0.5
故答案為：（0，0.5）
點(diǎn)評：本題考查指數(shù)函數(shù)、對數(shù)函數(shù)的單調(diào)性及應(yīng)用．對于復(fù)合函數(shù)問題一般轉(zhuǎn)化為初等函數(shù)解決．