English

Which of the Following Graphs Represents a One-one Function? - Mathematics

Advertisements
Advertisements

Question

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

Short/Brief Note
Advertisements

Solution

In the graph of (b), different elements on the x-axis have different images on the y-axis. But in (a), the graph cuts the x-axis at 3 points, which means that 3 points on the x-axis have the same image as 0 and hence, it is not one-one.
shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Functions - Exercise 2.5 [Page 73]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 2 Functions
Exercise 2.5 | Q 2 | Page 73

RELATED QUESTIONS

Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is a bijective function.


Let fR → be defined as f(x) = 10x + 7. Find the function gR → R such that g o f = f o = 1R.


Show that the function f : R → R given by f(x) = x3 is injective.


Given examples of two functions fN → N and gN → N such that gof is onto but is not onto.

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


Which of the following functions from A to B are one-one and onto?

 f2 = {(2, a), (3, b), (4, c)} ; A = {2, 3, 4}, B = {abc}


Classify the following function as injection, surjection or bijection :

 f : R → R, defined by f(x) = x3 − x


If f : R → R be the function defined by f(x) = 4x3 + 7, show that f is a bijection.


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


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.


Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.


Consider f : R → R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with inverse f−1 of f given by f−1 `(x)= sqrt (x-4)` where R+ is the set of all non-negative real numbers.


Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {abc}.


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

If f(x) = x + 7 and g(x) = x − 7, x ∈ R, write fog (7).


What is the range of the function

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


Let 

\[A = \left\{ x \in R : - 1 \leq x \leq 1 \right\} = B\] Then, the mapping\[f : A \to \text{B given by} f\left( x \right) = x\left| x \right|\] is 

 


If the function\[f : R \to \text{A given by} f\left( x \right) = \frac{x^2}{x^2 + 1}\] is a surjection, then A =

 

 


If  \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to


Which function is used to check whether a character is alphanumeric or not?


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


Let A be a finite set. Then, each injective function from A into itself is not surjective.


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

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:

g(x) = |x|


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


The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.


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


Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) 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}

  • Mr. ’X’ and his wife ‘W’ both exercised their voting right in the general election-2019, Which of the following is true?

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Raji wants to know the number of functions from A to B. How many number of functions are possible?

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?

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 : N → R be defined by f(x) = x2. Range of the function among the following is ____________.

If `f : R -> R^+  U {0}` be defined by `f(x) = x^2, x ∈ R`. The mapping is


`x^(log_5x) > 5` implies ______.


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 ______.


Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.


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

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×