Home
Class 12
MATHS
Let f and g be real valued functions def...

Let f and g be real valued functions defined as
`f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):}`
The value of (gof) (0) + (fog) (-3) is

A

-8

B

0

C

8

D

16

Text Solution

Verified by Experts

The correct Answer is:
B
`(gof)(0)=g(f(0))=g(7(0)^(2)+0-8)`
`=g(-8)=|-8|=8`
and `(fog)(-3)=f(g(-3))=f(0)=7(0)^(2)+0-8=-8`
`therefore (gof)(0)+(fog)(-3)=-8+8=0`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|5 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|2 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|3 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then

Knowledge Check

  • Let f and g be real valued functions defined as f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):} The value of 4(gof) (2) - (fog) (9) is

    A
    0
    B
    2
    C
    5
    D
    9

  • Let f and g be real valued functions defined as f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):} The value of 2(fog) (7) - (gof) (6) is

    A
    9
    B
    11
    C
    13
    D
    15

  • Let f g be functions from R to R defined as f (x) ={{:( 7x ^(2) + x - 8 "," x le 1),( 4x + 5"," 1 lt x le 7"," g (x) = ),(78x + 3"," x gt 7):}{{:(|x|"," x lt -3),(0"," -3 le x lt 2),(x ^(2) + 4"," x ge 2):} Then

    A
    (fog) `(-3) = 8`
    B
    (fog) `(9) = 683`
    C
    (gof) `(0) =- 8`
    D
    (gof) `(6) = 427`

    • Similar Questions

    Explore conceptually related problems

    If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

    The function f(x) = {(x+2, ",",1 le x lt 2),(4, ",", x = 2 ),(3x-2, ",", x gt 2 ):} is continuous at

    If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

    Two functions are defined as f(x)= {:{(x+1,"if" x le1),(2x+1,"if" lt x le 2):} g(x)= {:{(x^(2),"if" -1 le x lt 2),(x+2,"if" 2 le x le 3):}

    The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 lt x lt 2):}

    Home
    Profile