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    19-Jan-2017
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    Education

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  • 9o

    1

    . 1.

    ) f(x) = +

    2

    3 2x 4

    x 6x 11x 6 ii) f(x) = 3 2 x 1 iii) f(x) = +32 log (x 2)

    iv) f(x) = log x ( log4(3-x2)) v) =2

    f 5x x(x) log 4 vi) f(x) =

    24 x12

    vii) f(x) 5 x 4= + viii) = 3 2f(x) x 1 x 2. R f(x) = ln ( x2+2x+9) = R

    3. R

    : )f (x)=+

    24 - x(x - 1) x 1

    ) f (x)= 2x - 2 - 1

    + 34 - x - x

    ) f (x) =2x - x

    x - 2 - 1 + 1

    3x - 8 - x

    ) f (x) = 5x - 3 - 1

    ) f (x) = log (x2 + x - 2) + log +x 33 - x

    ) f (x) = xe - 1 + 1 - lnx ) f (x) = x2x - 1

    + 1x - 1

    , x [0, 2]

    . 4. C f , : I) f(x) = x2-5x+6 ii) 3xf(x) e 1= iii) 5f(x) log (x 3) 1= iv) f(x) x 3 2= 5. f (x) = x2 - 3x + 2. ) f (1), f (0), f (-3), f (2) ) Cf ) f (t), f (xt), f (x + h), x, t, h R.

    6. f (x) = x 1

    lnx . ) f. ) f (x) = e x . )

    7. ( ) ln( 1) f x k x= + + 2 1e 2 . : i) , R

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    2

    ii) fc 3 .

    8. , :f g R R , : = + 2( ) ( ) 4f x g x x x R . fc gc .

    9. , :f g R R : + + = 2 2( ) ( ) 1 2( ( ) ( ))f x g x f x g x , x R

    10. x R f g

    ( ) ( )( ) ( )( ) ( ) ( ) ( )

    2 2

    2

    3 2

    x +2x+3 -x -x-2

    -x-1 2x

    i) f x = x +2x+1 g x = x +2x+1

    ii) f x = e g x = e

    v) f x = ln e +1 g x = ln e +1

    11. :f R R : 2 2( 2) f(3 x) 0f x + + = , x R . f .

    12. ) + += =

    2

    2 3x 2 x 2xf(x) , g(x)x 1 x x

    ) + += =

    x 3 x 3f(x) , g(x)x 2x 2

    ) = + = + f(x) x 4 x 5 , g(x) x 5 4 x

    13. f (x) = x + 1. ) f.

    f1 (x) = 2x - 1

    x - 1 f2(x)=

    ++

    3

    2x 1

    x - x 1 f3 (x) = ( )2+x 1

    f4 (x) = x (x 1 + 1) f5 (x) = lnex+1 f6 (x) = eln (x+1)

    ) R .

    15. . f (x) = +x 1x - 1

    , g(x)=2+ +2

    22x 2x

    (x - 1),R, x > 0.

    ) f, g ) f = g; . f=g .

    .

  • 9o

    3

    f g , : =( ) ( )f x g x .

    i) =

    2

    21( ) xf x

    x x = + 1( ) 1g x

    x

    ii) =

    2( ) ln

    1xf x

    x = ( ) 2ln ln(1 )g x x x

    16.

    + += =

    2

    2x 3x 1, x [0,2] , x ( 2,1)3x 6f(x) g(x)2x 3 , x (2,6) x 1 x [1,13]

    2f+3g, f.g , f 2g

    17. f (x) =x,

    +

    >

    2x 1, x 2 x 2

    g (x) = ,

    <

    0, 0

    g(x)1, 0

    = >

    : ) f g !!!!!!!!!!!!!!

    .

    19. = +f(x) x 3 = g(x) ln(x 2) . f g . g f . f f v. g g 20. f g, g f, f f, g g

    21. f i) = + 2 ,(f g)(x) x x 3 g(x)=x-1

    .

    + > += =+ +

    2x 3, x 0x 1, x [1, )f(x) , g(x)2X 3. x ( ,1) 3x 1 x, x 0

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    ii) = + + 2 4 ,(f g)(x) 3 x x g(x) = x2 iii) = + = (g f)(x) 5x 4, g(x) 7x 6

    22. f [0, 2].

    : ) f (x2) ) f (x - 4) ) f (lnx) ) 2f( 1 x ), ) f(3 x 2) ) f( 3 x)

    x 3+

    23. [ ]: 2,1f R

    : = ( ) (2 3)g x xf , 2( ) ( )h x f x= ( ) (ln )q x f x=

    24. : (0,1] Rf . ( ) ( 2) (ln )g x f x f x= +

    25. 2( )2

    xf xx

    =

    ( ) 1g x x= .

    : ,f g g f 1ff

    26. x R + =3 3f(x) x ( ) =f f (x) x

    27. f ,

    + = f(x) 12f 3, x Rx x

    f.

    28. f(x)

    ( ) ( ) ( )( ) ( )

    ( )

    2 3 6 3

    2 x 2

    I) f 2x -1 = x -3x+2 II) f x = x -2x +1 x >0

    III) f lnx = x - x+2 IV) f e -1 = x -3x+1

    V) f(ln2x) = x+3 x >0

    29. = 2 1( ( )) xf f x x R

    : ) (2 1) 2 ( ) 1f x f x = , x R ) ( ) 1f x = .

    30. f : R R, + +f( ) f() f() , . ) .f(x) 0 ) )f() f() f( ,R.

    31. ( ) = + x ef g (x) e x = > .g(x) lnx 1, x 0 f 32. = f(x) g(x) x = 2g(x) x f(x), x R,

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    = (f g)(x) (g f )(x) xf(x) 33. f : R R = + 2f(x 1) 2f(3 x) x 1, x R. ) = + +2f(x) 2f(2 x) x 2x 2 ) = +2f(2 x) 2f(x) x 6x 10. ) f

    34. f 2f (x) - 3f ( 1x

    ) = x2, x0, f (2).

    35. = +2f(f(x)) x x 1 .f(1) 36. = f(f(x)) 3x 2 = f(3x 2) 3f(x) 2, x R

    37. : 3 1, 1( )2 , 1x x

    f xx x

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    ) f gc c .

    ) ( )( ) , 0( )

    f xh x xg x

    = > hc

    ,x >0 .

    44. f : R R (0) 0f =

    =

    ( )( ) ,1x

    f xg x x Re

    . ( ) 0g x < 0x .

    45. (1,5)A (5,-2) . : ) f . ) f f ( (e )) 2xf f < .

    46. f : R R :

    + = + >( ln ) ( 1) ln 3, 0f x x f x x x . f , ( ) 2f x = ( 1) 2xf e < .

    47. f : R R f ( ,0] f . :

    ) + = +( ) (5 ) (3 ) (7 )f x f x f x f x ) + = +5 3 7( ) ( ) ( ) ( )x x x xf e f e f e f e

    48. f :R R . :

    ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( )( )2

    . f x > f 3 . f 2x+1 0 . f f 3x -1 < f f 2x+5

    49. ( ) 1-x 1f x = e + -2 , x >0x

    .

    . f ( )0,+ . ( )0,+ : 1-xxe -2x +1>0 50. . ( ) ( )xf x = e +ln x+1 -1 . . . . : ( )2x 2e +ln x +1 >1 51. [ ) f : 0,+ R ( ) ( )2f x =3x+ln x +1 x>0 . . .

  • 9o

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