English

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

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

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.5 | Q 2 | Page 73

RELATED QUESTIONS

Check the injectivity and surjectivity of the following function:

f : Z → Z given by f(x) = x2


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]?


Classify the following function as injection, surjection or bijection :

 f : Z → Z, defined by f(x) = x − 5 


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = `x/(x^2 +1)`


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


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


Find gof and fog when f : R → R and g : R → R is defined by  f(x) = x2 + 8 and g(x) = 3x3 + 1 .


If f : R → (−1, 1) defined by `f (x) = (10^x- 10^-x)/(10^x + 10 ^-x)` is invertible, find f−1.


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


If f : R → R is defined by f(x) = 10 x − 7, then write f−1 (x).


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


Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not.


 \[f : A \to \text{B given by } 3^{ f\left( x \right)} + 2^{- x} = 4\] is a bijection, then

 

 

 

 


\[f : R \to R\] is defined by

\[f\left( x \right) = \frac{e^{x^2} - e^{- x^2}}{e^{x^2 + e^{- x^2}}} is\]

 


Let  \[f\left( x \right) = \frac{\alpha x}{x + 1}, x \neq - 1\] Then, for what value of α is \[f \left( f\left( x \right) \right) = x?\]

 


Let A = ℝ − {3}, B = ℝ − {1}. Let f : A → B be defined by \[f\left( x \right) = \frac{x - 2}{x - 3}, \forall x \in A\] Show that f is bijective. Also, find
(i) x, if f−1(x) = 4
(ii) f−1(7)


Let A = R − (2) and B = R − (1). If f: A ⟶ B is a function defined by`"f(x)"=("x"-1)/("x"-2),` how that f is one-one and onto. Hence, find f−1. 


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


Write about strlen() function.


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 R be the set of real numbers and f: R → R be the function defined by f(x) = 4x + 5. Show that f is invertible and find f–1.


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

f = {(1, 4), (1, 5), (2, 4), (3, 5)}


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

f(x) = `x/2`


If f(x) = (4 – (x – 7)3}, then f–1(x) = ______.


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


The function f : R → R given by f(x) = x3 – 1 is ____________.


The domain of the function `"f"("x") = 1/(sqrt ({"sin x"} + {"sin" ( pi + "x")}))` where {.} denotes fractional part, is


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 ____________.

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: {1,2,3,....} → {1,4,9,....} be defined by f(x) = x2 is ____________.

'If 'f' is a linear function satisfying f[x + f(x)] = x + f(x), then f(5) can be equal to:


Difference between the greatest and least value of f(x) = `(1 + (cos^-1x)/π)^2 - (1 + (sin^-1x)/π)^2` is ______.


Let f(1, 3) `rightarrow` R be a function defined by f(x) = `(x[x])/(1 + x^2)`, where [x] denotes the greatest integer ≤ x, Then the range of f is ______.


Let f(x) = ax (a > 0) be written as f(x) = f1(x) + f2(x), where f1(x) is an even function and f2(x) is an odd function. Then f1(x + y) + f1(x – y) equals ______.


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(x) be a polynomial of degree 3 such that f(k) = `-2/k` for k = 2, 3, 4, 5. Then the value of 52 – 10f(10) is equal to ______.


ASSERTION (A): The relation f : {1, 2, 3, 4} `rightarrow` {x, y, z, p} defined by f = {(1, x), (2, y), (3, z)} is a bijective function.

REASON (R): The function f : {1, 2, 3} `rightarrow` {x, y, z, p} such that f = {(1, x), (2, y), (3, z)} is one-one.


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


Which condition represents an into function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×