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 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.

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.

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.

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.

Let f(x) = x - 1/x , then f' (-1) is

Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f (x) = (x)/(1 + |x|), x in R is one one and onto function.

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

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

Show that the Modulus Functions f : R to R, given by f (x) =|x|, is neither one-one nor onto, whre |x| is x, if x is positive or 0 and |x| is -x, if x is negative.

Show that f:[-1,1] to R given by f(x) = x/(x + 2) is one-one. Find the inverse of the function f: [-1,1] to S ,where S is the range of f.