Show that f : N → N, given by f(x)=x+1,if xis odd, and x−1,if x is even. Is both one-one and onto.

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

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

check that f : N- N defined by f(n)={(n+1)/2,(if n is odd)),(n/2,(if n is even)) is one -one onto function ?

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.

Show that the function f: R->R given by f(x)=cosx for all x in R , is neither one-one nor onto.

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

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

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

Show that the function f: RvecR given by f(x)=cosxfora l lx in R , is neither one-one nor onto

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