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

Show that f : NvecN , given by f(x)={x+, if x i s od dx-1, if x i s e v e n is both one-one and onto.

Let f:N rarr N given by f(x)=x+(-1)^(x+1), then

Show that the function f:N rarr Z, defined by f(n)=(1)/(2)(n-1) when n is odd ;-1/2 n when n is even is both one-one and onto

If f:NrarrN is given by f(x)={((x+1)/(2), if x " is odd"),((x)/(2),if x " is even"):} and g:NrarrN is given by g(x)=x-(-1)^x, then f(g(x)) is (a) one one and onto (b) may one and onto (c) one one and not onto (d) neither one-one onto

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

Show that f:R rarr R, given by f(x)=x-[x], is neither one-one nor onto.

Show that f:R rarr R, given by f(x)=x-[x], is neither one-one nor onto.

Show that f:R rarr R, given by f(x)=x-[x], is neither one-one nor onto.

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