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 lt0):}` is neither one-one nor onto.

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.

Find Lt_(x to 0)f(x) where f(x)={{:(x-1,if gt0),(0, if x=0),(x+1, if x gt 0):}

If f: R to R defined by f(x) ={{:(2x+5, if, x gt 0),(3x-2, if, x le 0):} then f is

Show that the function f given by f(x)= {{:(x^3+3," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

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 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 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.