Home
Class 12
MATHS
Consider f : {1, 2, 3}->{a , b , c}given...

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`.

Text Solution

Verified by Experts

The correct Answer is:
`f ^(-1) `given by `f ^(-1) (a) = 1, f ^(-1) (b) =2 and f ^(-1) (c ) =3.`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.4|13 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise MISCLELLANEOUS EXERCISE ON CHAPTER 1|19 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

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

Let f: {1, 2, 3} rarr {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} rarr {1,2,3} such that gof =I_(x) and fog = I_Y , where X = {1,2,3} and Y = {a,b,c} ,

If f'(x)=sqrtx and f(1)=2 then find f(x).

If f(x)= (x-1)/(x+1) , Then show that f(-(1)/(x))= (-1)/(f(x))

If f(x)= (x-1)/(x+1) , Then show that f((1)/(x))= -f(x)

Consider f : R rarr R given by f(x) = 4x +3. Show that f is invertible. Find inverse of f .

Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} defined as f (1) =a, f (2) =b, f (3)=c, g (a) = apple, g (b) = ball and g (c )= cat. Show that f, g and gof are invertible. Find out f ^(-1) , g ^(-1) and ("gof")^(-1) and show that ("gof") ^(-1) =f ^(-1) og ^(-1).

If f'(x)=1-(4)/(x^(2)) and f(1)=6 then find f(x) and f(2).

If f(x)= x^(3)- (1)/(x^(3)) then show that f(x)+ f((1)/(x))= 0

Consider f : R_(+) rarr [-5,oo) given by f(x) = 9x^(2) +6x-5 . Show that f is invertible with f^(-1)(y) = ((sqrt(y+6)-1)/3)