Advertisements
Advertisements
प्रश्न
Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.
पर्याय
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
Given, A = {0, 1}
f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N
Thus range of f is {0, 1}
So, the mapping f: N → A is onto.
APPEARS IN
संबंधित प्रश्न
Check the injectivity and surjectivity of the following function:
f : N → N given by f(x) = x3
Check the injectivity and surjectivity of the following function:
f : Z → Z given by f(x) = x3
Prove that the greatest integer function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
Give an example of a function which is one-one but not onto ?
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = sin2x + cos2x
Set of ordered pair of a function? If so, examine whether the mapping is injective or surjective :{(x, y) : x is a person, y is the mother of x}
If f : A → B and g : B → C are onto functions, show that gof is a onto function.
Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.
Consider f : R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^-1 (x) = (sqrt (x +6)-1)/3 .`
Consider the function f : R+ → [-9 , ∞ ]given by f(x) = 5x2 + 6x - 9. Prove that f is invertible with f -1 (y) = `(sqrt(54 + 5y) -3)/5` [CBSE 2015]
Let A and B be two sets, each with a finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.
If A = {1, 2, 3} and B = {a, b}, write the total number of functions from A to B.
Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\] be a function defined by f(x) = cos [x]. Write range (f).
If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).
If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).
If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then find fog. [NCERT EXEMPLAR]
If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]
Let
\[f : R \to R\] be a function defined by
The function
Which of the following functions from
\[A = \left\{ x \in R : - 1 \leq x \leq 1 \right\}\]
The distinct linear functions that map [−1, 1] onto [0, 2] are
Let [x] denote the greatest integer less than or equal to x. If \[f\left( x \right) = \sin^{- 1} x, g\left( x \right) = \left[ x^2 \right]\text{ and } h\left( x \right) = 2x, \frac{1}{2} \leq x \leq \frac{1}{\sqrt{2}}\]
Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R. Then, show that f is one-one.
Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1
Let f: R → R be given by f(x) = tan x. Then f–1(1) is ______.
The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.
Let g(x) = x2 – 4x – 5, then ____________.
The function f: R → R defined as f(x) = x3 is:
A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}
- Three friends F1, F2, and F3 exercised their voting right in general election-2019, then which of the following is true?
An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.
Ravi decides to explore these sets for various types of relations and functions.
- Let R: B → G be defined by R = { (b1,g1), (b2,g2),(b3,g1)}, then R is ____________.
Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x2.
Answer the following questions using the above information.
- Let f: R → R be defined by f(x) = x2 is:
If f: R → R given by f(x) =(3 − x3)1/3, find f0f(x)
If f; R → R f(x) = 10x + 3 then f–1(x) is:
The solution set of the inequation log1/3(x2 + x + 1) + 1 > 0 is ______.
Let f(1, 3) `rightarrow` R be a function defined by f(x) = `(x[x])/(1 + x^2)`, where [x] denotes the greatest integer ≤ x, Then the range of f is ______.
Let f(x) be a polynomial of degree 3 such that f(k) = `-2/k` for k = 2, 3, 4, 5. Then the value of 52 – 10f(10) is equal to ______.
The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x; is continuous at ______.
Find the domain of sin–1 (x2 – 4).
