Home
Class 12
MATHS
Let f: {1, 3, 4}-> {1, 2, 5}and g: {1, 2...

Let `f: {1, 3, 4}-> {1, 2, 5}`and `g: {1, 2, 5} ->{1, 3}`be given by `f = {(1, 2), (3, 5), (4, 1)}`and `g = {(1, 3), (2, 3), (5, 1)}`. Write down `gof`.

Text Solution

Verified by Experts

`f: {1, 3, 4} to {1, 2, 5}`
and `g : {1, 2, 5} to {1, 3}`
and `f = {(1, 2), (3, 5), (4, 1)}`
and `g= {(1, 3), (2, 3), (5, 1)}`
`therefore (gof) (1) = g{f(1)} = g(2) = 3`
`" " (gof) (3) = g{f(3)} = g(5) = 1 `
`" " (gof) (4) = g{f(4)} = g(1) = 3 `
`therefore gof = { (1, 3), (3, 1), (4, 3)}`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.4|13 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.2|12 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

If the mapping f:{1,\ 3,\ 4}->{1,\ 2,\ 5} and g:{1,\ 2,\ 5}->{1,\ 3} , given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} and g={(2,\ 3),\ (5,\ 1),\ (1,\ 3)} , write fogdot

Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and g ={(1,\ 3),\ (3,\ 3),\ (4,\ 9),\ (5,\ 9)} find fog and gofdot

Knowledge Check

  • For f(x)=3x^(2)+4,g(x)=2, and h={(1,1),(2,1),(3,2)}

    A
    f is the only function
    B
    h is the only function
    C
    f and g are the only functions
    D
    f, g, and h are all functions

    • Similar Questions

    Explore conceptually related problems

    If f={(1,4),(2,5),(3,6)} and g={(4,8),(5,7),(6,9)} , then gof is

    If the functions f and g are given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} and g={(2,\ 3),\ (5,\ 1),\ (1,\ 3)} , find range of f and g . Also, write down fog and gof as sets of ordered pairs.

    If the functions f and g are given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} and g={(2,\ 3),\ (5,\ 1),\ (1,\ 3)} , find range of f and g . Also, write down fog and gof as sets of ordered pairs.

    If f and g two functions are defined as : f= {(1,2),(3,6),(4,5)} and g = {(2,3),(6,7),(5,8)}, then find gof.

    Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11 , 15 , 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)} . Are the following true?(i) f is a relation from A to B(ii) f is a function from A to B.Justify y

    Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11 , 15 , 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)} . Are the following true?(i) f is a relation from A to B(ii) f is a function from A to B.Justify y

    Let f\ a n d\ g be two real function given by f={(0,1),\ (2,0),\ (3,-4),\ (4,2),\ (5,1)a n d\ g={(1,0),\ (2,2),\ (3,-1),\ (4,4),\ (5,3)}dot Find the domain of fgdot

    Home
    Profile