English

Write the Total Number of One-one Functions from Set a = {1, 2, 3, 4} to Set B = {A, B, C}.

Advertisements
Advertisements

Question

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

Advertisements

Solution

has 4 elements and B has 3 elements.
Also, one-one function is only possible from A to B if (A≤ (B).
But, here n if (A) > (B).
So, the number of one-one functions from A to B is 0.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Functions - Exercise 2.5 [Page 73]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.5 | Q 5 | Page 73

RELATED QUESTIONS

Check the injectivity and surjectivity of the following function:

f : Z → Z given by f(x) = x2


Let S = {abc} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.

F = {(a, 2), (b, 1), (c, 1)}


Prove that the function f : N → N, defined by f(x) = x2 + x + 1, is one-one but not onto


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


Classify the following function as injection, surjection or bijection :

f : Q − {3} → Q, defined by `f (x) = (2x +3)/(x-3)`


Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = 5x3 + 4


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 .`


If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.


if f (x) = `sqrt (x +3) and  g (x) = x ^2 + 1` be two real functions, then find fog and gof.


Let

f (x) =`{ (1 + x, 0≤ x ≤ 2) , (3 -x , 2 < x ≤ 3):}`

Find fof.


Consider f : {1, 2, 3} → {abc} and g : {abc} → {apple, ball, cat} defined as f (1) = af (2) = bf (3) = cg (a) = apple, g (b) = ball and g (c) =  cat. Show that fg and gof are invertible. Find f−1g−1 and gof−1and show that (gof)−1 = f 1o g−1


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


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.


Which of the following graphs represents a one-one function?


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


Let f : R → R+ be defined by f(x) = axa > 0 and a ≠ 1. Write f−1 (x).


If f(x) = x + 7 and g(x) = x − 7, x ∈ R, write fog (7).


Let A = {abcd} and f : A → A be given by f = {( a,b ),( b , d ),( c , a ) , ( d , c )} write `f^-1`. [NCERT EXEMPLAR]


The function f : R → R defined by

`f (x) = 2^x + 2^(|x|)` is 

 


Let the function

\[f : R - \left\{ - b \right\} \to R - \left\{ 1 \right\}\]

\[f\left( x \right) = \frac{x + a}{x + b}, a \neq b .\text{Then},\]

 


If the function\[f : R \to \text{A given by} f\left( x \right) = \frac{x^2}{x^2 + 1}\] is a surjection, then A =

 

 


The distinct linear functions that map [−1, 1] onto [0, 2] are


Let [x] denote the greatest integer less than or equal to x. If \[f\left( x \right) = \sin^{- 1} x, g\left( x \right) = \left[ x^2 \right]\text{  and } h\left( x \right) = 2x, \frac{1}{2} \leq x \leq \frac{1}{\sqrt{2}}\]

 


Mark the correct alternative in the following question:
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is


Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.
{(x, y): x is a person, y is the mother of x}


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

h(x) = x|x|


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 ____________.


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

  • Let f: R → R be defined by f(x) = x2 is:

Let f: R → R defined by f(x) = 3x. Choose the correct answer


A function f: x → y is/are called onto (or surjective) if x under f.


Let f: R→R be defined as f(x) = 2x – 1 and g: R – {1}→R be defined as g(x) = `(x - 1/2)/(x - 1)`. Then the composition function f (g(x)) is ______.


If log102 = 0.3010.log103 = 0.4771 then the number of ciphers after decimal before a significant figure comes in `(5/3)^-100` is ______.


`x^(log_5x) > 5` implies ______.


Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is ______.


A function is a rule that assigns each element of one set to exactly how many elements of another set?


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


A function is onto when every element of the codomain has:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×