मराठी

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

Advertisements
Advertisements

प्रश्न

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

रिकाम्या जागा भरा
Advertisements

उत्तर

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Solved Examples [पृष्ठ १०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 1 Relations And Functions
Solved Examples | Q 27 | पृष्ठ १०

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Check the injectivity and surjectivity of the following function:

f : N → N given by f(x) = x2


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.


Let A = {–1, 0, 1, 2}, B = {–4, –2, 0, 2} and f, g : A → B be functions defined by f(x) = x2 – x, x ∈ A and g(x) = `2|x - 1/2| – 1`, x ∈ A. Are f and g equal?

Justify your answer. (Hint: One may note that two functions f : A → B and g : A → B such that f(a) = g(a) ∀ a ∈ A are called equal functions.)


Let fR → R be the Signum Function defined as

f(x) = `{(1,x>0), (0, x =0),(-1, x< 0):}`

and gR → be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0, 1]?


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) = sin2x + cos2x


If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.


Give examples of two one-one functions f1 and f2 from R to R, such that f1 + f2 : R → R. defined by (f1 + f2) (x) = f1 (x) + f2 (x) is not one-one.


Let f : N → N be defined by

`f(n) = { (n+ 1, if n  is  odd),( n-1 , if n  is  even):}`

Show that f is a bijection. 

                      [CBSE 2012, NCERT]


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


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

.


Find fog and gof  if : f(x) = sin−1 x, g(x) = x2


Let A = {1, 2, 3, 4}; B = {3, 5, 7, 9}; C = {7, 23, 47, 79} and f : A → Bg : B → C be defined as f(x) = 2x + 1 and g(x) = x2 − 2. Express (gof)−1 and f−1 og−1 as the sets of ordered pairs and verify that (gof)−1 = f−1 og−1.


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


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


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


Write the domain of the real function

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

 


Let

\[f : R \to R\]  be a function defined by

\[f\left( x \right) = \frac{e^{|x|} - e^{- x}}{e^x + e^{- x}} . \text{Then},\]
 

Mark the correct alternative in the following question:

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


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,

 


Which function is used to check whether a character is alphanumeric or not?


Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is ______.


Let f: R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and – 3, respectively, are ______.


Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1 


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


Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) 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 ____________.


Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

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

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • Let f: R → R be defined by f(x) = x − 4. Then the range of f(x) 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 ____________.

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


The function defined by \[\mathrm{f}(x)=\frac{2x+3}{3x+4},x\neq-\frac{4}{3}\] is


A function is called many-one if two or more different elements of the domain have:


A perfect one-to-one matching between users and unique IDs is similar to:


Which condition represents a one-one (injective) function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×