Home
Class 12
MATHS
Let f: W ->Wbe defined as f(n) = n - 1,...

Let `f: W ->W`be defined as `f(n) = n - 1`, if `n` is odd and `f(n) = n + 1`, if `n` is even. Show that `f` is invertible. Find the inverse of `f`. Here, `W` is the set of all whole numbers.

Text Solution

AI Generated Solution

To show that the function \( f: W \to W \) defined by \[ f(n) = \begin{cases} n - 1 & \text{if } n \text{ is odd} \\ n + 1 & \text{if } n \text{ is even} \end{cases} ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise SOLVED EXAMPLES|50 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.4|13 Videos

  • PROBABILITY

    NCERT|Exercise EXERCISE 13.2|18 Videos

  • SETS

    NCERT|Exercise EXERCISE 1.3|1 Videos

Similar Questions

Explore conceptually related problems

Let f:W rarr W, be defined as f(x)=x-1, if x is odd and f(x)=x+1, if x is even.Show that f is invertible.Find the inverse of f, where W is the set of all whole numbers.

Y={n^(2):n in N}in N Consider f:N rarr Y as Show that f is invertible.Find the inverse of f.

Let f:N rarr N be defined by: f(n)={n+1,quad if n is oddn -1,quad if n is even Show that f is a bijection.

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

Let f:N->N be defined as f(n)= (n+1)/2 if n is odd and f(n)=n/2 if n is even for all ninN State whether the function f is bijective. Justify your answer

Let f" ":" "N ->R be a function defined as f(x)=4x^2+12 x+15 . Show that f" ":" "N-> S , where, S is the range of f, is invertible. Find the inverse of f.

Let f:N uu{0}rarr N uu{0} be defined by f(n)={n+1, if n is eve nn-1,quad if quad n is odd Show that f is a bijection.

Let f : N rarr N be defined as f(x) = 2x for all x in N , then f is