English

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

Advertisements
Advertisements

Question

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

Options

  • One-one

  • Onto

  • Bijective

  • F is not defined

MCQ
Fill in the Blanks
Advertisements

Solution

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
  Is there an error in this question or solution?
Chapter 1: Relations And Functions - Exercise [Page 15]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 12
Chapter 1 Relations And Functions
Exercise | Q 37 | Page 15

RELATED QUESTIONS

Let f : R → R be defined as f(x) = x4. Choose the correct answer.


Let S = {a, b, c} and T = {1, 2, 3}. Find F−1 of the following functions F from S to T, if it exists.

F = {(a, 2), (b, 1), (c, 1)}


Let f: R → R be the Signum Function defined as

f(x) = `{(1,x>0), (0, x =0),(-1, x< 0):}`

and g: R → R be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0, 1]?


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 : Z → Z given by f(x) = x2


Classify the following function as injection, surjection or bijection :

f : Z → Z, defined by f(x) = x2 + x


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = sinx


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


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.


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


Find fog and gof  if : f (x) = |x|, g (x) = sin x .


Find fog and gof  if : f (x) = x+1, g(x) = `e^x`

.


Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1


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 : R → (0, 2) defined by `f (x) =(e^x - e^(x))/(e^x +e^(-x))+1`is invertible , find f-1.


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


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


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


If f : C → C is defined by f(x) = x4, write f−1 (1).


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


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


Write the domain of the real function f defined by f(x) = `sqrt (25 -x^2)`   [NCERT EXEMPLAR]


Let f, g : R → R be defined by f(x) = 2x + l and g(x) = x2−2 for all x

∈ R, respectively. Then, find gof.  [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


Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is ______.


Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is ______.


Consider the set A containing n elements. Then, the total number of injective functions from A onto itself is ______


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.


Which of the following functions from Z into Z are bijections?


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


Given a function If as f(x) = 5x + 4, x ∈ R. If g : R → R is inverse of function ‘f 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.

  • The function f: Z → Z defined by f(x) = x2 is ____________.

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


Let A = {1, 2, 3, ..., 10} and f : A `rightarrow` A be defined as

f(k) = `{{:(k + 1, if k  "is odd"),(     k, if k  "is even"):}`.

Then the number of possible functions g : A `rightarrow` A such that gof = f is ______.


Let A = R – {2} and B = R – {1}. If f: A `→` B is a function defined by f(x) = `(x - 1)/(x - 2)` then show that f is a one-one and an onto function.



The given function f : R → R is not ‘onto’ function. Give reason.


In the function from \(X\) to \(Y\), if \(6\in Y\) is not the image of any element of \(X\), the function is:


Which condition represents an into function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×