Home
Class 12
MATHS
Let f:{1,2,3} to {a,b,c} be one-one and ...

Let `f:{1,2,3} to {a,b,c}` be one-one and onto function given by `f (1) =a, f (2) =b and f (3) =c.` Show that there exists a function `g : {a,b,c} to {1,2,3}` such that gof `=I _(x) and ` fog `=I _(y),` where, `X = {1,2,3} and Y={a,b,c}.`

Text Solution

Verified by Experts

The correct Answer is:
`I _(y)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT TAMIL|Exercise EXERCISE 1.1|9 Videos

  • RELATIONS AND FUNCTIONS

    NCERT TAMIL|Exercise EXERCISE 1.2|7 Videos

  • PROBABILITY DISTRIBUTIONS

    NCERT TAMIL|Exercise EXERCISE 11.6 (Choose the Correct )|19 Videos

  • THEORY OF EQUATIONS

    NCERT TAMIL|Exercise EXERCISE 3.7|10 Videos

Similar Questions

Explore conceptually related problems

Show that an onto function f: {1,2,3} to {1,2,3} is always one-one.

Show that a one-one function f: {1,2,3} to {1,2,3} must be onto.

Let A={0, 1, 2, 3} and B={1, 2, 3, 5, 7, 9} be two sets. Let f: A to B be a function given by f(x)=2x+1 . Represents this function as a table

Let A={0, 1, 2, 3} and B={1, 2, 3, 5, 7, 9} be two sets. Let f: A to B be a function given by f(x)=2x+1 . Represents this function as an arrow

Let A={0, 1, 2, 3} and B={1, 2, 3, 5, 7, 9} be two sets. Let f: A to B be a function given by f(x)=2x+1 . Represents this function as a graph

If A={-3,-2,-1,0,1,2,3} and f : A->B is an onto function defined by f(x)=2x^2+x-2 and find B .

If A={-2,-1,0,1,2} and f:A to B is an onto function defined by f(x)=x^(2) +x+1 then find B .

If A={-2,-1,0,1,2} and f : A->B is an onto function defined by f(x)=x^2+x+1 and find B .

Let f and g be function continuous in [a,b] and differentiable on [a,b] .If f(a)=f(b)=0 then show that there is a point c in (a,b) such that g'(c) f(c)+f'(c)=0 .