मराठी

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

Advertisements
Advertisements

प्रश्न

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

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

बेरीज
Advertisements

उत्तर

Given, X = {1, 2, 3} and Y = {4, 5}

So, X × Y = {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}

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

f is not a function as f(1) = 4 and f(1) = 5

Hence, pre-image ‘1’ has not unique image.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Exercise [पृष्ठ ११]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 1 Relations And Functions
Exercise | Q 12. (i) | पृष्ठ ११

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Check the injectivity and surjectivity of the following function:

f : N → N given by f(x) = x2


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

f : R → R defined by f(x) = 1 + x2


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


Give an example of a function which is neither one-one nor onto ?


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


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


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


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 = {0, −1, −3, 2}; B = {−9, −3, 0, 6} and f(x) = 3 x.


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


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


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


Let f  be a function from C (set of all complex numbers) to itself given by f(x) = x3. Write f−1 (−1).


Write the domain of the real function

`f (x) = 1/(sqrt([x] - x)`.


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


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]


If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]


Which of the following functions form Z 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


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

\[f\left( n \right)\begin{cases}\frac{n - 1}{2}, & \text{when n is odd} \\ - \frac{n}{2}, & \text{when n is even}\end{cases}\]

 


Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.


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.


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


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


Let A = R – {3}, B = R – {1}. Let f : A → B be defined by `"f"("x") = ("x" - 2)/("x" - 3)` Then, ____________.


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: N → N be defined by f(x) = x2 is ____________.

If f: R → R given by f(x) =(3 − x3)1/3, find f0f(x)


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


If f; R → R f(x) = 10x + 3 then f–1(x) is:


The domain of the function `cos^-1((2sin^-1(1/(4x^2-1)))/π)` is ______.


Let x is a real number such that are functions involved are well defined then the value of `lim_(t→0)[max{(sin^-1  x/3 + cos^-1  x/3)^2, min(x^2 + 4x + 7)}]((sin^-1t)/t)` where [.] is greatest integer function and all other brackets are usual brackets.


Let f(1, 3) `rightarrow` R be a function defined by f(x) = `(x[x])/(1 + x^2)`, where [x] denotes the greatest integer ≤ x, Then the range of f 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 ______.


Which one of the following graphs is a function of x?

Graph A Graph B

The trigonometric equation tan–1x = 3tan–1 a has solution for ______.


The function defined by \[\mathrm{f}(x)=\frac{2x+3}{3x+4},x\neq-\frac{4}{3}\] is


Let f: R→Rbe defined as f (x) = `(x^2 + 1)/2`, then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×