Show that the function f:N to N, given b...

Show that the function `f:N to N,` given by `f (1) =f (2) =1 and f (x) =x -1,` for every `x gt 2,` is onto but not one-one.

Verified by Experts

The correct Answer is:

`f (1) =1`

Similar Questions

Explore conceptually related problems

Show that the function f:NtoN given by f(1)=f(2)=1 and f(x)=x-1 for every xgt2 is on to but not one -one.

Show that the function f:N to N given by f (x) =2x is one - one but not onto

Show that the function f: N to N given by f(x)=2x is one-one but not onto.

Prove that the function f: R to R, given by f (x) =2x, is one-one and onto.

Show that the signum function f : R to R given by f(x) = {(1, if, x gt 0),(0, if, x = 0),(-1, if, x lt 0):} is neither one-one nor onto.

Check the continuity of the function f given by f(x) = 2x + 3 at x = 1 .

Show that f:Nto N, given by x + 1, if x is odd, f (x) = x -1, if x is even is both one-one and onto.

Show that the function f : N to N defined by f(x) = x^(2), AA x in N is injective but not surjective.

Show that the Modulus function f : R to R given by f (x) = [x] is neither one-one nor onto.

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.