मराठी

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

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • One-one

  • Onto

  • Bijective

  • F is not defined

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

Let f: R → R be defined by f(x) = `1/x` ∀ x ∈ R. Then f is f is not defined.

Explanation:

We have, f(x) = `1/x` ∀ x ∈ R

For x = 0, f(x) is not defined.

Hence, f(x) is a not define function.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Exercise [पृष्ठ १५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 1 Relations And Functions
Exercise | Q 37 | पृष्ठ १५

व्हिडिओ 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`


Which of the following functions from A to B are one-one and onto?
 f1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7}


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


Classify the following function as injection, surjection or bijection :

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


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


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


Show that the logarithmic function  f : R0+ → R   given  by f (x)  loga x ,a> 0   is   a  bijection.


If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.


Show that f : R→ R, given by f(x) = x — [x], is neither one-one nor onto.


Let f : N → N be defined by

`f(n) = { (n+ 1, if n  is  odd),( n-1 , if n  is  even):}`

Show that f is a bijection. 

                      [CBSE 2012, NCERT]


Consider f : N → N, g : N → N and h : N → R defined as f(x) = 2x, g(y) = 3y + 4 and h(z) = sin z for all x, y, z ∈ N. Show that ho (gof) = (hog) of.


Give examples of two functions f : N → N and g : N → N, such that gof is onto but f is not onto.


Find fog and gof  if : f(x) = sin−1 x, g(x) = x2


A function f : R → R is defined as f(x) = x3 + 4. Is it a bijection or not? In case it is a bijection, find f−1 (3).


Let f : R `{- 4/3} `- 43 →">→ R be a function defined as f(x) = `(4x)/(3x +4)` . Show that f : R - `{-4/3}`→ Rang (f) is one-one and onto. Hence, find f -1.


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


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


Write whether f : R → R, given by `f(x) = x + sqrtx^2` is one-one, many-one, onto or into.


Let f be an injective map with domain {x, y, z} and range {1, 2, 3}, such that exactly one of the following statements is correct and the remaining are false.

\[f\left( x \right) = 1, f\left( y \right) \neq 1, f\left( z \right) \neq 2 .\]

The value of

\[f^{- 1} \left( 1 \right)\] is 

 


Which of the following functions from

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

 


 Let
\[g\left( x \right) = 1 + x - \left[ x \right] \text{and} f\left( x \right) = \begin{cases}- 1, & x < 0 \\ 0, & x = 0, \\ 1, & x > 0\end{cases}\] where [x] denotes the greatest integer less than or equal to x. Then for all \[x, f \left( g \left( x \right) \right)\] is equal to


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


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


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)}


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

h(x) = x|x|


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


Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x4, is ____________.


The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.


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?

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 find the number of injective functions from B to G. How many numbers of injective functions are possible?

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • Let f: R → R be defined by f(x) = x − 4. Then the range of f(x) is ____________.

Function f: R → R, defined by f(x) = `x/(x^2 + 1)` ∀ x ∈ R is not


Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.


Let f: R→R be a continuous function such that f(x) + f(x + 1) = 2, for all x ∈ R. If I1 = `int_0^8f(x)dx` and I2 = `int_(-1)^3f(x)dx`, then the value of I1 + 2I2 is equal to ______.


If A = {x ∈ R: |x – 2| > 1}, B = `{x ∈ R : sqrt(x^2 - 3) > 1}`, C = {x ∈ R : |x – 4| ≥ 2} and Z is the set of all integers, then the number of subsets of the set (A ∩ B ∩ C) C ∩ Z is ______.


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


A function is called one-one if different elements of the domain have:


A function is called bijective if it is both:


Let \(X=\{-1,2,5,8,11\}\), \(Y=\{4,6,8\}\), and suppose different elements \(2,5,8\) of \(X\) have the same image \(4\). What type of function is it with respect to the one-one property?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×