Question

若函數(shù)是函數(shù)的反函數(shù)，其圖象過點(diǎn)，且函數(shù)在區(qū)間上是增函數(shù)，則正數(shù)的取值范圍是                 ．

Answer 1

解析試題分析：由題意可得，所以函數(shù)，由該函數(shù)在區(qū)間上是增函數(shù)，得函數(shù)在區(qū)間上為增函數(shù)，且，考慮到函數(shù)在上單調(diào)遞增，所以當(dāng)時(shí)，有得，當(dāng)時(shí)，有即得，從而求得所求正數(shù)的取值范圍為.
考點(diǎn)：1.反函數(shù)；2.函數(shù)的單調(diào)性；3.對(duì)數(shù)函數(shù)；4.常用函數(shù).