English

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

Advertisements
Advertisements

Question

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

Fill in the Blanks

Solution

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

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 27 | Page 10

RELATED QUESTIONS

Let A and B be sets. Show that f: A × B → B × A such that (a, b) = (b, a) is bijective function.


Let A = {−1, 0, 1} and f = {(xx2) : x ∈ A}. Show that f : A → A is neither one-one nor onto.


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


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


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 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.


If f : Q → Qg : Q → Q are two functions defined by f(x) = 2 x and g(x) = x + 2, show that f and g are bijective maps. Verify that (gof)−1 = f−1 og −1.


If A = {1, 2, 3} and B = {ab}, write the total number of functions from A to B.


If f : C → C is defined by f(x) = x2, write f−1 (−4). Here, C denotes the set of all complex numbers.


Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x3. Write f−1(1).


Let f : R → Rg : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 − x2. Write fog (−2).


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]


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

 

 

 
 

Which of the following functions from

\[A = \left\{ x : - 1 \leq x \leq 1 \right\}\]

to itself are bijections?

 

 

 


Let

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


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

 


If f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)` then verify that `("fog") (x)` = x.


Let R be the set of real numbers and f: R → R be the function defined by f(x) = 4x + 5. Show that f is invertible and find f–1.


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


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

The domain of function is f(x) = `sqrt(-log_0.3(x - 1))/sqrt(x^2 + 2x + 8)` is ______.


The graph of the function y = f(x) is symmetrical about the line x = 2, then ______.


If A = {x ∈ R: |x – 2| > 1}, B = `{x ∈ R : sqrt(x^2 - 3) > 1}`, C = {x ∈ R : |x – 4| ≥ 2} and Z is the set of all integers, then the number of subsets of the set (A ∩ B ∩ C) C ∩ Z is ______.


Let a function `f: N rightarrow N` be defined by

f(n) = `{:[(2n",", n = 2","  4","  6","  8","......),(n - 1",", n = 3","  7","  11","  15","......),((n + 1)/2",", n = 1","  5","  9","  13","......):}`

then f is ______.


If f : R `rightarrow` R is defined by `f(x) = (2x - 7)/4`, show that f(x) is one-one and onto.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×