मराठी

ASSERTION (A): The relation f : {1, 2, 3, 4} → {x, y, z, p} defined by f = {(1, x), (2, y), (3, z)} is a bijective function. REASON (R): The function f : {1, 2, 3} → {x, y, z, p} - Mathematics

Advertisements
Advertisements

प्रश्न

ASSERTION (A): The relation f : {1, 2, 3, 4} {x, y, z, p} defined by f = {(1, x), (2, y), (3, z)} is a bijective function.

REASON (R): The function f : {1, 2, 3} {x, y, z, p} such that f = {(1, x), (2, y), (3, z)} is one-one.

पर्याय

  • Both (A) and (R) are true and (R) is the correct explanation of (A).

  • Both (A) and (R) are true but (R) is not the correct explanation of (A).

  • (A) is true but (R) is false.

  • (A) is false but (R) is true.

MCQ

उत्तर

(A) is false but (R) is true.

Explanation:

Assertion is false. As element 4 has no image under f, so relation f is not a function.

Reason is true. The given function f : {1, 2, 3} {x, y, z, p} is one – one, as for each a ∈ {1, 2, 3}, there is different image in {x, y, z, p} under f.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2023-2024 (March) Board Sample Paper

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Check the injectivity and surjectivity of the following function:

f: R → R given by f(x) = x2


Following the case, state whether the function is one-one, onto, or bijective. Justify your answer.

f: → R defined by f(x) = 1 + x2


Show that the function f: ℝ → ℝ defined by f(x) = xx2+1, xRis neither one-one nor onto. Also, if g: ℝ → ℝ is defined as g(x) = 2x - 1. Find fog(x)


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


Let A = [-1, 1]. Then, discuss whether the following functions from A to itself is one-one, onto or bijective : h(x) = x2 


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


Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.


Find f −1 if it exists : f : A → B, where A = {1, 3, 5, 7, 9}; B = {0, 1, 9, 25, 49, 81} and f(x) = x2


Let f : R {-43}- 43 →">→ R be a function defined as f(x) = 4x3x+4 . Show that f : R - {-43}→ Rang (f) is one-one and onto. Hence, find f -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:[π2,π2] A be defined by f(x) = sin x. If f is a bijection, write set A.


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


The function f : R → R defined by

f(x)=2x+2|x| is 

 


Which of the following functions from

A={x:1x1}

to itself are bijections?

 

 

 


Let

A={x:1x1}andf:AA such that f(x)=x|x|

 


If a functionf:[2,) to B defined by f(x)=x24x+5 is a bijection, then B =


Let  f(x)=x2andg(x)=2x Then, the solution set of the equation

fog(x)=gof(x) is 



Let A = R − (2) and B = R − (1). If f: A ⟶ B is a function defined byf(x)=x-1x-2, how that f is one-one and onto. Hence, find f−1


For sets A, B and C, let f: A → B, g: B → C be functions such that g o f is surjective. Then g is surjective.


Let f: R – {35} → R be defined by f(x) = 3x+25x-3. Then ______.


The function f : R → R defined by f(x) = 3 – 4x 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: {1,2,3,....} → {1,4,9,....} be defined by f(x) = x2 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:


Let a and b are two positive integers such that b ≠ 1. Let g(a, b) = Number of lattice points inside the quadrilateral formed by lines x = 0, y = 0, x = b and y = a. f(a, b) = [ab]+[2ab]+...+[(b-1)ab], then the value of [g(101,37)f(101,37)] is ______.

(Note P(x, y) is lattice point if x, y ∈ I)

(where [.] denotes greatest integer function)


Let f(n) = [13+3n100]n, where [n] denotes the greatest integer less than or equal to n. Then n=156f(n) is equal to ______.


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


Let a function f:NN be defined by

f(n) = [2n,n=2, 4, 6, 8,......n-1,n=3, 7, 11, 15,......n+12,n=1, 5, 9, 13,......

then f is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.