मराठी

What is the Range of the Function `F (X) = ([X - 1])/(X -1) ?`

Advertisements
Advertisements

प्रश्न

What is the range of the function

`f (x) = ([x - 1])/(x -1) ?`

Advertisements

उत्तर

` f (x) = ([x - 1])/(x - 1) = (+(x-1)) /(x-1)` = ±1

Range of f = {-1 ,1 }

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Functions - Exercise 2.5 [पृष्ठ ७४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 2 Functions
Exercise 2.5 | Q 33 | पृष्ठ ७४

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

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


Give an example of a function which is one-one but not onto ?


Let A = {−1, 0, 1} and f = {(xx2) : x ∈ A}. Show that f : A → A is neither one-one nor 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 : N → N given by f(x) = x3


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


Set of ordered pair of  a function? If so, examine whether the mapping is injective or surjective :{(xy) : x is a person, y is the mother of x}


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


Give examples of two surjective functions f1 and f2 from Z to Z such that f1 + f2 is not surjective.


Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:
(i) an injective map from A to B
(ii) a mapping from A to B which is not injective
(iii) a mapping from A to B.


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = 2x + x2 and  g(x) = x3


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


Find fog and gof  if : f (x) = x2 g(x) = cos x .


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


Consider f : R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^-1 (x) = (sqrt (x +6)-1)/3 .`


Let A = R - {3} and B = R - {1}. Consider the function f : A → B defined by f(x) = `(x-2)/(x-3).`Show that f is one-one and onto and hence find f-1.

                    [CBSE 2012, 2014]


If f : R → R is given by f(x) = x3, write f−1 (1).


Write the domain of the real function

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


The function f : R → R defined by

`f (x) = 2^x + 2^(|x|)` is 

 


The range of the function

\[f\left( x \right) =^{7 - x} P_{x - 3}\]

 


Which of the following functions form Z to itself are bijections?

 

 

 
 

Let

\[A = \left\{ x : - 1 \leq x \leq 1 \right\} \text{and} f : A \to \text{A such that f}\left( x \right) = x|x|\]

 


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  \[f\left( x \right) = x^2 and g\left( x \right) = 2^x\] Then, the solution set of the equation

\[fog \left( x \right) = gof \left( x \right)\] is 



If \[g \left( f \left( x \right) \right) = \left| \sin x \right| \text{and} f \left( g \left( x \right) \right) = \left( \sin \sqrt{x} \right)^2 , \text{then}\]

 


Let

\[A = \left\{ x \in R : x \leq 1 \right\} and f : A \to A\] be defined as

\[f\left( x \right) = x \left( 2 - x \right)\] Then,

\[f^{- 1} \left( x \right)\] is


Mark the correct alternative in the following question:

Let f : → R be given by f(x) = tanx. Then, f-1(1) is

 

 


If f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)` then verify that `("fog") (x)` = x.


Let f, g: R → R be two functions defined as f(x) = |x| + x and g(x) = x – x ∀ x ∈ R. Then, find f o g and g o f


Let f: R → R be the function defined by f(x) = 2x – 3 ∀ x ∈ R. write f–1 


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}


Using the definition, prove that the function f: A→ B is invertible if and only if f is both one-one and onto


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?

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.

  • The function f: R → R defined by f(x) = x − 4 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: N → N be defined by f(x) = x2 is ____________.

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


Let f: R→R be a polynomial function satisfying f(x + y) = f(x) + f(y) + 3xy(x + y) –1 ∀ x, y ∈ R and f'(0) = 1, then `lim_(x→∞)(f(2x))/(f(x)` is equal to ______.


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

Graph A Graph B

A function is called many-one if two or more different elements of the domain have:


Which condition represents a many-one function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×