Given examples of two functions `f: N ->N a n dg: N->N`such that g o f is ontobut f is not onto. (Hint: Consider `f(x) = x+1 a n dg(x) = |x|`) .

Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such that g o f is onto but f is not onto. (Hint: Consider f(x)" "= x+1 a n d""""""""g(x)" "=" "|x| ) .

Give examples of two functions f : N to N and g : N to N such g o f is onto but f is not onto.

Give examples of two functions f : N to N and g : N to N such g o f is onto but f is not onto.

Give examples of two function f: N rarr N and g : N rarr N such that gof is onto but f is not onto. (Hint: Consider f(x) = x+1 " and "g(x) = {x-1 if x>1 1 if x=1.

Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such that of is onto but f is not onto. (Hint: Consider f(x)" "=" "x+1" "a n d""""""""g(x)" "=" "{x-1 if x>1 1 if x=1}

Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that go f is injective but g is not injective. (Hint: Consider f(x)" "=" "x" "a n d""""""""g(x)" "=" "|x| )

Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o f is injective but is not injective. (Hint: Consider f(x)" "=" "x" "a n d""""""""g(x)" "=" "|x| )

Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-one but not onto.

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

Prove that the function f:N rarr N so that f(x)=2x^(2)-1 is one-one but not onto.