Show that the function f: N`rarr` 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 rarr N, given by f(n)=n- (-1)^(n), AA n in N is a bijection.

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

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

Show that the function f :R rarr R, given by f(x) = cos x, AA x in R is neither one-one nor onto.

Show that the function f: R rarr R , f(x)= x^(4) is many-one and into.

Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][x^2], xne0),(0, x=0):} is onto but not one-to-one.

Show that the fuction f:RrarrR defined by f (x)=sin x is neither one-one nor onto.

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

State whether the function f : R rarr R, defined by f(x) = 3 - 4x is onto or not.

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