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

AI Generated Solution

To solve the problem, we need to find the inverse of the function \( f \) defined as follows: - \( f: \{1, 2, 3\} \rightarrow \{a, b, c\} \) - \( f(1) = a \) - \( f(2) = b \) - \( f(3) = c \) ### Step 1: Finding \( f^{-1} \) ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise Exercise 1.1|16 Videos

  • PROBABILITY

    NCERT ENGLISH|Exercise EXERCISE 13.2|18 Videos

  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 11.3|14 Videos

Similar Questions

Explore conceptually related problems

Given f(x)=3x+2 . Find f^(-1)(x)

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=I_y

Let f : R rarr given by f(x) = 3x^(2) + 5x + 1 . Find f(0), f(1), f(2).

If f(x) = ax^2+bx+c and f(1)=3 and f(-1)=3, then a+c equals

If f:R->R be defined by f(x)=x^2+1 , then find f^(-1)(17) and f^(-1)(-3) .

Using matrix method, find the quadratic defined by f(x) = ax^(2) + bx + c if f(1) = 0, f(2) = -2 and f(3) = -6. Hence find the value of f(-1).

Consider the function f:R -{1} given by f (x)= (2x)/(x-1) Then f^(-1)(x) =

Consider f:{1,\ 2,\ 3}->{a ,\ b ,\ c} and g:{a ,\ b ,\ c}-> {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\ a n d\ gof are invertible. Find f^(-1),\ g^(-1) and (gof)^(-1) and show that (gof)^(-1)=f^(-1)o\ g^(-1) .

If f: C->C is defined by f(x)=(x-2)^3 , write f^(-1)(-1) .

If f(x)=1-4x , and f^(-1)(x) is the inverse of f(x), then f(-3)f^(-1)(-3)=