हिंदी

Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective.{(a, b): a is a person, b is an ancestor of a} - Mathematics

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

Given, {(a, b): a is a person, b is an ancestor of a}

It’s clearly seen that any person ‘a’ has more than one ancestors.

Thus, it does not represent a function.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Exercise [पृष्ठ ११]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 1 Relations And Functions
Exercise | Q 8. (ii) | पृष्ठ ११

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`


Classify the following function as injection, surjection or bijection : f : N → N given by f(x) = x3


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


Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`


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


Let f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3) (4, 9) (5, 9)}. Show that gof and fog are both defined. Also, find fog and gof.


Verify associativity for the following three mappings : f : N → Z0 (the set of non-zero integers), g : Z0 → Q and h : Q → R given by f(x) = 2xg(x) = 1/x and h(x) = ex.


If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?


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


Let f : [−1, ∞) → [−1, ∞) be given by f(x) = (x + 1)2 − 1, x ≥ −1. Show that f is invertible. Also, find the set S = {x : f(x) = f−1 (x)}.


If f : A → Ag : A → A are two bijections, then prove that fog is an injection ?


If f : A → Ag : A → A are two bijections, then prove that fog is a surjection ?


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


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


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


Write the domain of the real function

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


If f : R → R is defined by f(x) = 3x + 2, find f (f (x)).


Let f : R → R be the function defined by f(x) = 4x − 3 for all x ∈ R Then write f .   [NCERT EXEMPLAR]


Let M be the set of all 2 × 2 matrices with entries from the set R of real numbers. Then, the function f : M→ R defined by f(A) = |A| for every A ∈ M, is

 


A function f  from the set of natural numbers to integers defined by

`{([n-1]/2," when  n is  odd"   is ),(-n/2,when  n  is  even ) :}`

 

 


The function

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

Which of the following functions from

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

 


If \[f : R \to R\] is given by \[f\left( x \right) = x^3 + 3, \text{then} f^{- 1} \left( x \right)\] is equal to

 


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,

 


A function f: R→ R defined by f(x) = `(3x) /5 + 2`, x ∈ R. Show that f is one-one and onto. Hence find f−1.


Write about strcmp() function.


Let A be a finite set. Then, each injective function from A into itself is not surjective.


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


Let A = R – {3}, B = R – {1}. Let f: A → B be defined by f(x) = `(x - 2)/(x - 3)` ∀ x ∈ A . Then show that f is bijective.


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

g(x) = |x|


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 – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then ______.


Let f : R → R be defind by f(x) = `1/"x"  AA  "x" in "R".` Then f is ____________.


Let g(x) = x2 – 4x – 5, then ____________.


Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` then f is ____________.


Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x3 + 5. The function (fog)-1 (x) is equal to ____________.


Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Raji wants to know the number of functions from A to B. How many number of functions are possible?

An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

  • Ravi wants to know among those relations, how many functions can be formed from B to G?

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(x) be a polynomial of degree 3 such that f(k) = `-2/k` for k = 2, 3, 4, 5. Then the value of 52 – 10f(10) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×