English

Set of ordered pairs a function ? If so, examine whether the mapping is injective or surjective :{(a, b) : a is a person, b is an ancestor of a}

Advertisements
Advertisements

Question

Set of ordered pair of a function ? If so, examine whether the mapping is injective or surjective :{(a, b) : a is a person, b is an ancestor of a} 

Sum
Advertisements

Solution

g = {(a, b) : a is a person, b is an ancestor of a}
Since, the ordered map (a, b) does not map 'a' - a person to a living person.
So, g is not a function.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Functions - Exercise 2.1 [Page 32]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.1 | Q 9.2 | Page 32

RELATED QUESTIONS

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


Find the number of all onto functions from the set {1, 2, 3, ..., n} to itself.


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


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = sinx


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


Show that the function f : R − {3} → R − {2} given by f(x) = `(x-2)/(x-3)` is a bijection.


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x and g(x) = |x| .


 If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x|- x, ∀x∈R" .Then find fog and gof. Hence find fog(–3), fog(5) and gof (–2).


Which one of the following graphs represents a function?


If A = {a, b, c} and B = {−2, −1, 0, 1, 2}, write the total number of one-one functions from A to B.


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


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


Let `f : R - {- 3/5}` → R be a function defined as `f  (x) = (2x)/(5x +3).` 

f-1 : Range of f → `R -{-3/5}`.


Let f : R → R be defined as  `f (x) = (2x - 3)/4.` write fo f-1 (1) .


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


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


If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).


If f(x) = 4 −( x - 7)3 then write f-1 (x).


Which of the following functions from

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

to itself are bijections?

 

 

 


The function

\[f : R \to R\] defined by\[f\left( x \right) = \left( x - 1 \right) \left( x - 2 \right) \left( x - 3 \right)\]

(a) one-one but not onto
(b) onto but not one-one
(c) both one and onto
(d) neither one-one nor onto


Let

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

\[f\left( x \right) = \frac{x - m}{x - n}, \text{where} \ m \neq n .\] Then,
 

The function

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

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  \[f : R \to \left( - 1, 1 \right)\] is defined by

\[f\left( x \right) = \frac{- x|x|}{1 + x^2}, \text{ then } f^{- 1} \left( x \right)\] equals

 


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

 


If  \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to


Write about strlen() function.


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


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


Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not

h = {(1,4), (2, 5), (3, 5)}


Using the definition, prove that the function f: A→ B is invertible if and only if f is both one-one and onto


Let f: R → R be defined by f(x) = `1/x` ∀ x ∈ R. Then f is ______.


The function f : R → R defined by f(x) = 3 – 4x is ____________.


The number of bijective functions from set A to itself when A contains 106 elements is ____________.


Which of the following functions from Z into Z is bijective?


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


Write the domain and range (principle value branch) of the following functions:

f(x) = tan–1 x.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×