题目

（本小题满分12分）已知函数，。 （1）若函数在区间上存在零点，求实数a的取值范围； （2）当时，若对任意的，总存在，使成立，求实数 的取值范围。 答案：解：（1）∵函数的对称轴是，            ∴函数在区间上是减函数………………1分 又∵函数在区间上存在零点，则必有 即，解得………………4分 故所求实数a的取值范围为。………………5分 （2）当时，若对任意的，总存在，使成立，只需函数的值域为函数的值域的子集。 而，的值域为，………………………………6分 下面求的值域。 ①当时，为常数，不符合题意舍去；……………………………7分 ②当时，函数在上为增函数，所以的值域为，要使，需，解得；……………………………9分 ③当时，函数在上为减函数，所以的值域为，要使，需，解得；………………………11分 综上所述，实数的取值范围为或。……………………………12分                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     

查看本题答案和解析