हिंदी

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions. - Mathematics

Advertisements
Advertisements

प्रश्न

For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is injective. Then both f and g are injective functions.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Solved Examples [पृष्ठ १०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 1 Relations And Functions
Solved Examples | Q 32 | पृष्ठ १०

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Show that the modulus function f : R → R given by f(x) = |x| is neither one-one nor onto, where |x| is x if x is positive or 0 and |x| is − x if x is negative.


Let A = R − {3} and B = R − {1}. Consider the function f : A → B defined by f(x) = `((x- 2)/(x -3))`. Is f one-one and onto? Justify your answer.


Show that the function f : R → {x ∈ R : −1 < x < 1} defined by f(x) = `x/(1 + |x|)`, x ∈ R is one-one and onto function.


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) = 3 − 4x


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 gof and fog when f : R → R and g : R → R is defined by  f(x) = x2 + 2x − 3 and  g(x) = 3x − 4 .


Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3) (4, 9) (5, 9)}. Show that gof and fog are both defined. Also, find fog and gof.


Let R+ be the set of all non-negative real numbers. If f : R+ → R+ and g : R+ → R+ are defined as `f(x)=x^2` and `g(x)=+sqrtx` , find fog and gof. Are they equal functions ?


Find fog and gof  if : f (x) = x+1, g (x) = sin x .


Find f −1 if it exists : f : A → B, where A = {0, −1, −3, 2}; B = {−9, −3, 0, 6} and f(x) = 3 x.


Let f be a function from R to R, such that f(x) = cos (x + 2). Is f invertible? Justify your answer.


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.


Which one of the following graphs represents a function?


If A = {abc} and B = {−2, −1, 0, 1, 2}, write the total number of one-one functions from A to B.


Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {abc}.


If f : R → R is defined by f(x) = x2, write f−1 (25)


Which one the following relations on A = {1, 2, 3} is a function?
f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)}                                                                                                        [NCERT EXEMPLAR]


The  function f : [-1/2, 1/2, 1/2] → [-π /2,π/2], defined by f (x) = `sin^-1` (3x - `4x^3`), is

 


If  \[f\left( x \right) = \sin^2 x\] and the composite function   \[g\left( f\left( x \right) \right) = \left| \sin x \right|\] then g(x) is equal to


Mark the correct alternative in the following question:

Let f : → R be given by f(x) = tanx. Then, f-1(1) is

 

 


Mark the correct alternative in the following question:
Let f : R→ R be defined as, f(x) =  \[\begin{cases}2x, if x > 3 \\ x^2 , if 1 < x \leq 3 \\ 3x, if x \leq 1\end{cases}\] 

Then, find f( \[-\]1) + f(2) + f(4)

 


Mark the correct alternative in the following question:
Let A = {1, 2, ... , n} and B = {a, b}. Then the number of subjections from A into B is


Mark the correct alternative in the following question:
Let f :  \[-\] \[\left\{ \frac{3}{5} \right\}\] \[\to\]  R be defined by f(x) = \[\frac{3x + 2}{5x - 3}\] Then,

 


Show that the function f: R → R defined by f(x) = `x/(x^2 + 1)`, ∀ ∈ + R , is neither one-one nor onto


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


Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

k = {(1,4), (2, 5)}


If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is ______.


Let f : R `->` R be a function defined by f(x) = x3 + 4, then f is ______.


Range of `"f"("x") = sqrt((1 - "cos x") sqrt ((1 - "cos x")sqrt ((1 - "cos x")....infty))`


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?

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Raji wants to know the number of functions from A to B. How many number of functions are possible?

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: N → N be defined by f(x) = x2 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.

  • The function f: Z → Z defined by f(x) = x2 is ____________.

If f: R → R given by f(x) =(3 − x3)1/3, find f0f(x)


Consider a function f: `[0, pi/2] ->` R, given by f(x) = sinx and `g[0, pi/2] ->` R given by g(x) = cosx then f and g are


Which one of the following graphs is a function of x?

Graph A Graph B

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×