मराठी

The domain of the function f: R → R defined by f(x) = x2-3x+2 is ______

Advertisements
Advertisements

प्रश्न

The domain of the function f: R → R defined by f(x) = `sqrt(x^2 - 3x + 2)` is ______

रिकाम्या जागा भरा
Advertisements

उत्तर

Here x2 – 3x + 2 ≥ 0

⇒ (x – 1)(x – 2) ≥ 0

⇒ x ≤ 1 or x ≥ 2

Hence the domain of f = `(– oo, 1] ∪ [2, oo)`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Solved Examples [पृष्ठ १०]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 1 Relations And Functions
Solved Examples | Q 26 | पृष्ठ १०

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Prove that the greatest integer function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.


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


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

(Hint: Consider f(x) = x and g(x) =|x|)


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

(Hint: Consider f(x) = x + 1 and `g(x) = {(x-1, ifx >1),(1, if x = 1):}`


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, 3), (b, 2), (c, 1)} 


Show that the function f : R − {3} → R − {2} given by f(x) = `(x-2)/(x-3)` is a bijection.


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


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


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.


  ` if  f : (-π/2 , π/2)` → R and g : [−1, 1]→ R be defined as f(x) = tan x and g(x) = `sqrt(1 - x^2)` respectively, describe fog and gof.


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 A and B be two sets, each with a finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.


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


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

Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\]  be a function defined by f(x) = cos [x]. Write range (f).


Let `f : R - {- 3/5}` → R be a function defined as `f  (x) = (2x)/(5x +3).` 

f-1 : Range of f → `R -{-3/5}`.


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


Which one the following relations on A = {1, 2, 3} is a function?
f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)}                                                                                                        [NCERT EXEMPLAR]


If a function\[f : [2, \infty )\text{ to B defined by f}\left( x \right) = x^2 - 4x + 5\] is a bijection, then B =


Which of the following functions from

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

 


\[f : Z \to Z\]  be given by

 ` f (x) = {(x/2, ", if  x is even" ) ,(0 , ", if  x  is  odd "):}`

Then,  f is


Let

\[f : [2, \infty ) \to X\] be defined by

\[f\left( x \right) = 4x - x^2\] Then, f is invertible if X =

 


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

g = {(1, 4), (2, 4), (3, 4)}


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

k = {(1,4), (2, 5)}


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

f(x) = `x/2`


Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.


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


Which of the following functions from Z into Z is bijective?


Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` then f is ____________.


The function f: R → R defined as f(x) = x3 is:


A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever


Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}

  • Three friends F1, F2, and F3 exercised their voting right in general election-2019, then which of the following is true?

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 ____________.

A function f: x → y is said to be one – one (or injective) if:


Let the function f: R → R be defined by f(x) = 4x – 1, ∀ x ∈ R then 'f' is


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 ______.


The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x; is continuous at ______.


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×