English

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

Question

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.

Options

  • True

  • False

MCQ
True or False

Solution

This statement is False.

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 32 | Page 10

RELATED QUESTIONS

Classify the following function as injection, surjection or bijection :  f : Z → Z given by f(x) = x2


Set of ordered pair of  a function? If so, examine whether the mapping is injective or surjective :{(xy) : x is a person, y is the mother of x}


Find gof and fog when f : R → R and g : R → R is  defined by  f(x) = 8x3 and  g(x) = x1/3.


Let f : R → R and g : R → R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.


Give examples of two functions f : N → Z and g : Z → Z, such that gof is injective but gis not injective.


Find fog and gof  if : f (x) = x2 g(x) = cos x .


If f(x) = |x|, prove that fof = f.


Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1


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


Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\]  be a function defined by f(x) = cos [x]. Write range (f).


Let \[f : \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right] \to\] A be defined by f(x) = sin x. If f is a bijection, write set A.


Let f : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]


Write the domain of the real function

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


Let

\[f : R \to R\]
\[f\left( x \right) = \frac{x^2 - 8}{x^2 + 2}\]
Then,  f is


The function

\[f : R \to R, f\left( x \right) = x^2\]
 

The function \[f : R \to R\] defined by

\[f\left( x \right) = 6^x + 6^{|x|}\] is 

 


The inverse of the function

\[f : R \to \left\{ x \in R : x < 1 \right\}\] given by

\[f\left( x \right) = \frac{e^x - e^{- x}}{e^x + e^{- x}}\] is 

 


Let  \[f\left( x \right) = \frac{1}{1 - x} . \text{Then}, \left\{ f o \left( fof \right) \right\} \left( x \right)\]

 


If  \[F : [1, \infty ) \to [2, \infty )\] is given by

\[f\left( x \right) = x + \frac{1}{x}, then f^{- 1} \left( x \right)\]

 


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)

 


Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

h(x) = x|x|


Let f: R → R be the functions defined by f(x) = x3 + 5. Then f–1(x) is ______.


If f(x) = (4 – (x – 7)3}, then f–1(x) = ______.


Let A = R – {3}, B = R – {1}. Let f : A → B be defined by `"f"("x") = ("x" - 2)/("x" - 3)` Then, ____________.


The function f : R → R given by f(x) = x3 – 1 is ____________.


Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation 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:

Let f: R → R defined by f(x) = x4. Choose the correct answer


If f: R→R is a function defined by f(x) = `[x - 1]cos((2x - 1)/2)π`, where [ ] denotes the greatest integer function, then f is ______.


Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×