Question

6.已知函數(shù)y=，
(1)求函數(shù)的定義域,值域;
(2)確定函數(shù)的單調(diào)區(qū)間.

Answer 1

(1)函數(shù)的定義域是R,此函數(shù)的值域?yàn)?0,).
(2)在區(qū)間(-∞,3］上是增函數(shù),在區(qū)間［3,+∞)上是減函數(shù).

(1)根據(jù)指數(shù)函數(shù)的定義域易知,此函數(shù)的定義域是R,先求出函數(shù)u=x²-6x+11在R上的值域,再利用指數(shù)函數(shù)的單調(diào)性求得此函數(shù)的值域?yàn)?0,).
(2)由函數(shù)y=與u=x²-6x+11在同一區(qū)間上的單調(diào)性相反,易得函數(shù)y=在區(qū)間(-∞,3］上是增函數(shù),在區(qū)間［3,+∞)上是減函數(shù).