Show that the function f : N→ N, given by f (1) = f(2) = 1 and f(x) = x – 1,for every x > 2, is onto but not one-one.

Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for every xgeq2 , is onto but not one-one.

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.

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

Consider the function f:R -{1} given by f (x)= (2x)/(x-1) Then f^(-1)(x) =

Show that the function f:NtoN defined by f(x)=2x-1 is one-one but not onto.

Show that the modulus function f: R->R , given by f(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 function f(x)=3x+ 2 is one-one and onto

Let f : {1, 2, 3}->{a , b , c} be one-one and onto function given by f (1) = a , f (2) = b and f (3) = c . Show that there exists a function g : {a , b , c}->{1, 2, 3} such that gof=I_x and fog=I_y