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

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.

Let f : Z to Z be given by f(x) = {((x)/(2) if"is even"),(0 if" is odd"):} Then f is

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

If f : R - (-1,1) to R is defined by f(x) = (x)/(x^(2)-1) , verify whether f is one to one.

If f:(-3,3)toA is given by f(x) = x^(3) + 2 . Find A so that f 'is onto.

Let f(x)=(x-1)^4(x-2)^n ,n in Ndot Then f(x) has a maximum at x=1 if n is odd a maximum at x=1 if n is even a minimum at x=1 if n is even a minima at x=2 if n is even

Let f: X rarr Y be a function defined by f(x) = a sin ( x + pi/4 ) + c. If f is both one-one and onto, then find the set X and Y