Let `f: Z->Z` be defined by `f(x)=x+2.` Find `g: Z->Z` such that `gof=I_Z` .

If f: Z->Z be defined by f(x)=2x for all x in Z . Find g: Z->Z such that gof=I_Z .

If f: Z->Z be defined by f(x)=2x for all x in Z . Find g: Z->Z such that gof=I_Z .

Let f : Z rarr Z be a function defined by f(n) =3n AA n in Z and g: Z rarrZ be defined by g(n) = {{:((n)/(3),"if n is a multiple of 3"),(""0, "if n is not a multiple of 3"):} Show that gof = I_(z) and fog ne I_(z) .

Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , is a function but not bijective function.

Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

If f: Z to Z be given by f(x)=x^(2)+ax+b , Then,

If f: Z to Z be given by f(x)=x^(2)+ax+b , Then,

Let f : Z rarr Z be defined as f(n) = 3n for all n in Z . Let g : Z rarr Z be defined as g(n)= n/3 if n is a multiple of 3. g(n)= 0 if n is not a multiple of 3. Show that gof = I_z and fog ne I_Z

Classify f: Z->Z , defined by f(x)=x^2+x as injection, surjection or bijection.

Show that the function f : Z to Z defined by f(x) = x^(3), AA x in Z is injective but not surjective.