Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Show that the function f: ℝ → ℝ defined by f(x) = `x/(x^2 + 1), ∀x in R`is neither one-one nor onto. Also, if g: ℝ → ℝ is defined as g(x) = 2x - 1. Find fog(x)

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

In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.

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