2017届高三数学一轮总复习第二章函数与基本初等函数ⅰ第三节函数的奇偶性及周期性课时跟踪检测理.doc

1、 1 1 f(x) 1 x x _ f(x) ( 0) (0 x f( x) 1 x x f(x) f(x) 2 y y _( ) y 1 x 2 y y 1 x f(x) 0 3 ) f(x) x (0 f(x) log2x f( 2) _. f(x) f( 2) f( 2) log2 2 1 2 . 1 24 f(x) 6,6 x 0,6 f(x) f(x)0 _ f(x) 6,0 ( ) f(x)0 6 2) (0,2) 6 2) (0,2) 5 f(x) R x0 f(x) x 1 x0 f(x) x 1 x0 f(x) f( x) ( x 1) 2 x0 _ f(x) f(x)0 (

2、 5 2) (0,2) ( 5 2) (0,2) 2 f(x) g(x) R h(x) f(x g(x) f(x) g(x) h(x) _ ( f(x) g(x) f( x) f(x) g( x) g(x) h( x) f( x)g( x) f(x)g(x) h(x) h(x) h(x) f(x) g(x) f(x) g(x) h(x) f(x) g(x) h(x) 3 f(x) ( x f(x 2) f(x) x 0,2) f(x) log2(x 1) f( 2 015) f(2 016) _ f(x) 2 f( 2 015) f(2 016) f(2 015) f(2 016) f(1)

3、f(0) x 0,2) f(x) log2(x 1) f( 2 015) f(2 016) 1 0 1. 1 4 y f(x) R x0 x0 2f(x) 10 x 10 x _ y f(x) (0 f 1 2 0 y f(x) ( 0) f 1 2 0 f(x)0 x 1 2 1 2 0 x x 1 21 2 . x 1 21 27 f(x) g(x) R f(x) g(x) 1 2 x f(1) g(0) g( 1) _ f(x) g(x) 1 2 x x x f( x) g( x) 2 x f(x) g(x) R f( x) f(x) g( x) g(x) f(x) g(x) 2 x .

4、 f(x) 2 x 2 x 2 g(x) 2 x 2 x 2 f(1) 3 4 g(0) 1 g( 1) 5 4 f(1)g(0)g( 1) 4 f(1)g(0)g( 1) 8 ) R f(x) f(x) f( x) 0 f(x) f(x 2) x f(x) 2 x 1 f 1 2 f(1) f 3 2 f(2) f 5 2 _. f(x) 2 f 1 2 f(1) f 3 2 f(2) f 5 2 f 1 2 f(1) f 1 2 f(0) f 1 2 f 1 2 f(1) f 1 2 f(0) f 1 2 f 1 2 f(1) f(0) 2 1 2 1 2 1 1 2 0 1 2. 2 9

5、 f(x) ( f(x) x 1 x 0,1 f(x) 2 x 1. (1) f(x) (2) x 1,2 f(x) (3) f(0) f(1) f(2) f(2 016) (1) f(x) f( x) f(x) f(x) x 1 f(2 x) f( x) f(x) f(4 x) f(2 x) 2 f(2 x) f(x) f(x) 4 (2) x 1,2 2 x 0,1 f(x) x 1 f(x) f(2 x) 2 2 x 1 x 1,2 (3) f(0) 0 f(1) 1 f(2) 0 f(3) f( 1) f(1) 1. f(x) 4 f(0) f(1) f(2) f(2 016) f(0

6、) 0. 10 ) f(x) x f(x) x x x x a x x3.5 (1) f( 2) (2) x3 f(x) f( x) ( x 3)(a x) (x 3)(a x) x3. a f(x) 0 3 2 3 2 5 g(a) f 3 2 9 4 . 30 f(2 x 2 )f(x) x _ x0 x0) f(x) x 3 x x x0. f(x) R f(2 x 2 )f(x) 2 x 2 x 2x1. x ( 2,1) ( 2,1) 2 ) f(x) R 0 a b R f(ab) af(b) bf(a) f(x) _( f( x) f ( x f(x) xf( 1) a b 1

7、f(1) f(1) f(1) f(1) 0. a b 1 f ( 1) f( 1) f( 1) f(1) 2f ( 1) f( 1) 0. f( x) f(x) 0 f(x) f(x) 3 f(x) D x|x x1 x2 D f(x1 x2) f(x1) f(x2) (1) f(1) (2) f(x) (3) f(4) 1 f(x 1)2, f(x) (0 x (1) x1 x2 D f(x1 x2) f(x1) f(x2) x1 x2 1 f(1) 2f(1) f(1) 0. (2)f(x) x1 x2 1 f(1) f( 1) f( 1) 7 f( 1) 1 2 f(1) 0. x1 1 x2 x f( x) f( 1) f(x) f( x) f(x) f(x) (3) f f(4) f(4) 2 (2) f(x) f(x 1)2 f(|x 1|)f(16) f(x) (0 0|x 1|16 15x17 x 1. x ( 15,1) (1,17)