मराठी

Let A be a finite set. Then, each injective function from A into itself is not surjective. - Mathematics

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प्रश्न

Let A be a finite set. Then, each injective function from A into itself is not surjective.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

This statement is False.

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पाठ 1: Relations And Functions - Solved Examples [पृष्ठ १०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 1 Relations And Functions
Solved Examples | Q 31 | पृष्ठ १०

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Check the injectivity and surjectivity of the following function:

f : Z → Z given by f(x) = x3


Show that the Signum Function f : R → R, given by `f(x) = {(1", if"  x > 0), (0", if"  x  = 0), (-1", if"  x < 0):}` is neither one-one nor onto.


In the following case, state whether the function is one-one, onto or bijective. Justify your answer.

f : R → R defined by f(x) = 1 + x2


Show that the function f : R → R given by f(x) = x3 is injective.


If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`


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 : Z → Z, defined by f(x) = x2 + x


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


Let A = [-1, 1]. Then, discuss whether the following functions from A to itself is one-one, onto or bijective : h(x) = x2 


Show that if f1 and f2 are one-one maps from R to R, then the product f1 × f2 : R → R defined by (f1 × f2) (x) = f1 (x) f2 (x) need not be one - one.


Find  fog (2) and gof (1) when : f : R → R ; f(x) = x2 + 8 and g : R → Rg(x) = 3x3 + 1.


Find fog and gof  if : f (x) = x+1, g(x) = `e^x`

.


Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.


A function f : R → R is defined as f(x) = x3 + 4. Is it a bijection or not? In case it is a bijection, find f−1 (3).


If f : R → R is given by f(x) = x3, write f−1 (1).


If f : C → C is defined by f(x) = (x − 2)3, write f−1 (−1).


If f : R → Rg : R → are given by f(x) = (x + 1)2 and g(x) = x2 + 1, then write the value of fog (−3).


Write the domain of the real function

`f (x) = sqrtx - [x] .`


Let f : R → R be the function defined by f(x) = 4x − 3 for all x ∈ R Then write f .   [NCERT EXEMPLAR]


The function f : R → R defined by

`f (x) = 2^x + 2^(|x|)` is 

 


The function 

f : A → B defined by 

f (x) = - x2 + 6x - 8 is a bijection if 

 

 

 

 


Let M be the set of all 2 × 2 matrices with entries from the set R of real numbers. Then, the function f : M→ R defined by f(A) = |A| for every A ∈ M, is

 


Let

\[A = \left\{ x \in R : x \leq 1 \right\} and f : A \to A\] be defined as

\[f\left( x \right) = x \left( 2 - x \right)\] Then,

\[f^{- 1} \left( x \right)\] is


Let  \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] Then, for what value of α is \[f \left( f\left( x \right) \right) = x?\]

 


Mark the correct alternative in the following question:
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is


Let A = R − (2) and B = R − (1). If f: A ⟶ B is a function defined by`"f(x)"=("x"-1)/("x"-2),` how that f is one-one and onto. Hence, find f−1


Let C be the set of complex numbers. Prove that the mapping f: C → R given by f(z) = |z|, ∀ z ∈ C, is neither one-one nor onto.


Let A = R – {3}, B = R – {1}. Let f: A → B be defined by f(x) = `(x - 2)/(x - 3)` ∀ x ∈ A . Then show that f is bijective.


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 ____________.


The function f : R → R defined by f(x) = 3 – 4x is ____________.


Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x4, is ____________.


Let g(x) = x2 – 4x – 5, then ____________.


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}

  • Mr. ’X’ and his wife ‘W’ both exercised their voting right in the general election-2019, 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.

  • Ravi wants to find the number of injective functions from B to G. How many numbers of injective functions are possible?

If f; R → R f(x) = 10x + 3 then f–1(x) is:


Let f(x) = ax (a > 0) be written as f(x) = f1(x) + f2(x), where f1(x) is an even function and f2(x) is an odd function. Then f1(x + y) + f1(x – y) equals ______.


For x ∈ R, x ≠ 0, let f0(x) = `1/(1 - x)` and fn+1 (x) = f0(fn(x)), n = 0, 1, 2, .... Then the value of `f_100(3) + f_1(2/3) + f_2(3/2)` is equal to ______.


The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x; is continuous at ______.


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