Home
Class 12
MATHS
[" 7.Give examples of two functions "f:N...

[" 7.Give examples of two functions "f:N rarr N" and "g:N rarr N" such that "g" of 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]]

Promotional Banner

Similar Questions

Explore conceptually related problems

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.

Give examples of two functions f:N rarr Z and g: Z rarr Z such that gof is injective but g is not injective. (Hint : Consider f(x) = x and g(x) = |x| ) .

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 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 functions f: N->Z" and "g: Z->Z such that gof is injective but g is not injective. (Hint: Consider f(x) = x" and "g(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->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| )

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| )

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