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

Let `f : {1, 2, 3}->{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}->{1, 2, 3}`such that `gof=I_x`and `fog=

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise QUESTIONS FROM NCERT EXEMPLAR|5 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (a) (Short Answer Type Questions)|13 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos
  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos
  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

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

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

Consider f" ":" "{1," "2," "3}->{a ," "b ," "c} given by f(1)" "=" "a , f(2)" "=" "b and f(3)" "=" "c . Find f^(-1) and show that (f^(-1))^(-1)=" "f .

Show that the function f(x)=3x+2 is one one and onto

Let f and g be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6 and g(1)=2. Show that there exists c in(0,1) such that f'(c)=2g'(c)

Letf: A rarr B be a function then show that f is a bijection if and only if there exists a function g:B rarr A such that fog =I_(B)&gof=I_(A)& in this case g=f^(-1)

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

If f:A rarr B and g:B rarr C are onto functions show that gof is an onto function.

Let f and g be real functions defined by f(x)=(x)/(x+1) and g(x)=(1)/(x+3). Describe the functions gof and fog( if they exist).