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22 2015

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1 - 22 2015

1. f : I R.() f I, ,

, , I, < < , f () pi f () f ().

50() pi f pipi . pi

f 1 1 f I. pi, - pi , pi pi- .

50

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pi :

1. () (): f , : , , I, < < , f() pi f() f()

pi.() (): :

, , I, < < , f() pi f() f() f I

f , pi , f() 6= f(). pi f() < f() x I, :i. < < x = f() < f() f(x)ii. < x < = f() < f(x) f()iii. x < < = f(x) f() < f():

< x = f() f(x) (1) x < = f(x) f() (2)

pi x, y I x < y. :i. x < < y 2= f(x) f() f(y) f(x) f(y)ii. x < y < 2= f(x) f(y) f() f(x) f(y)iii. < x < y 1= f() f(x) f(y) f(x) f(y), f() < f()

x, y I & x < y = f(x) f(y) = f , f() > f()

x, y I & x < y = f(x) f(y) = f

2. () (): f , :i. x < y = f(x) < f(y) f

ii. x < y = f(x) > f(y) f

, x 6= y f(x) 6= f(y) f 1 1

3 - 22 2015

() (): f 1 1, f () . pi:i. f ( ) pi x 6= y f(x) = f(y) f 1 1.

ii. f I ( pi - I, pi), pi pi pi:

< < f() f() f() (3)

, < < . f(), f(), f() R pi pi pi (3).. f() f() f(), pi (, )

f() = f(). , f 1 1. . f() f() f(), pi (, )

f() = f(). , f 1 1. pi, f .

pi pi pi, pi pi 1 1 () . pi:

f(x) =

x 0 x 1

x 1 1 < x < 2

f 11 [0, 2] [0, 2].

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