English

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

Advertisements
Advertisements

Question

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

Options

  • True

  • False

MCQ
True or False

Solution

This statement is True.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Relations And Functions - Solved Examples [Page 10]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 1 Relations And Functions
Solved Examples | Q 33 | Page 10

RELATED QUESTIONS

Check the injectivity and surjectivity of the following function:

f: Z → Z given by f(x) = x3


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


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 : R → R, defined by f(x) = 1 + x2


Show that the exponential function f : R → R, given by f(x) = ex, is one-one but not onto. What happens if the co-domain is replaced by`R0^+` (set of all positive real numbers)?


If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.


Suppose f1 and f2 are non-zero one-one functions from R to R. Is `f_1 / f^2` necessarily one - one? Justify your answer. Here,`f_1/f_2 : R → R   is   given   by   (f_1/f_2) (x) = (f_1(x))/(f_2 (x))  for all  x in R .`


Let f : R → R and g : R → R be defined by f(x) = + 1 and (x) = x − 1. Show that fog = gof = IR.


If f : R → (0, 2) defined by `f (x) =(e^x - e^(x))/(e^x +e^(-x))+1`is invertible , find f-1.


If f : A → Ag : A → A are two bijections, then prove that fog is an injection ?


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


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


If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).


Let A = {1, 2, 3, 4} and B = {ab} be two sets. Write the total number of onto functions from A to B.


Let fg : R → R be defined by f(x) = 2x + l and g(x) = x2−2 for all x

∈ R, respectively. Then, find gof.  [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]


The function f : R → R defined by

`f (x) = 2^x + 2^(|x|)` is 

 


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

 


Which of the following functions form Z to itself are bijections?

 

 

 
 

Let  \[f\left( x \right) = x^2 and g\left( x \right) = 2^x\] Then, the solution set of the equation

\[fog \left( x \right) = gof \left( x \right)\] is 



If \[g \left( f \left( x \right) \right) = \left| \sin x \right| \text{and} f \left( g \left( x \right) \right) = \left( \sin \sqrt{x} \right)^2 , \text{then}\]

 


Write about strcmp() function.


Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is ______.


Consider the set A containing n elements. Then, the total number of injective functions from A onto itself is ______


If f: R → R is defined by f(x) = x2 – 3x + 2, write f(f (x))


Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. 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?

A function f: x → y is said to be one – one (or injective) if:


Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.


Let A = R – {2} and B = R – {1}. If f: A `→` B is a function defined by f(x) = `(x - 1)/(x - 2)` then show that f is a one-one and an onto function.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×