PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Give an example of a function which is one-one but not onto ?

Give an example of a function which is not one-one but onto ?

Give an example of a function which is neither one-one nor onto ?

Which of the following functions from A to B are one-one and onto?
 f₁ = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7}

Which of the following functions from A to B are one-one and onto?

 f₂ = {(2, a), (3, b), (4, c)} ; A = {2, 3, 4}, B = {a, b, c}

 Which of the following functions from A to B are one-one and onto ?  

f₃ = {(a, x), (b, x), (c, z), (d, z)} ; A = {a, b, c, d,}, B = {x, y, z}. 

Prove that the function f : N → N, defined by f(x) = x² + x + 1, is one-one but not onto

Let A = {−1, 0, 1} and f = {(x, x²) : x ∈ A}. Show that f : A → A is neither one-one nor onto.

Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x²

Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x²

Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x³

Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x³

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = |x|

Classify the following function as injection, surjection or bijection :

f : Z → Z, defined by f(x) = x² + x

Classify the following function as injection, surjection or bijection :

 f : Z → Z, defined by f(x) = x − 5 

Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = sinx

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = x³ + 1

Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x³ − x

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = sin²x + cos²x

Classify the following function as injection, surjection or bijection :

f : Q − {3} → Q, defined by `f (x) = (2x +3)/(x-3)`