मराठी

Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective: k(x) = x2

Advertisements
Advertisements

प्रश्न

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

k(x) = x2 

बेरीज
Advertisements

उत्तर

Given, A = [–1, 1]

Let k(x1) = k(x2)

x12 = x22

x1 = ± x2

Therefore, k(x) is not one-one.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Exercise [पृष्ठ १२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 1 Relations And Functions
Exercise | Q 21. (iv) | पृष्ठ १२

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

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, defined by f(x) = x − 5 


If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.


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


Let R+ be the set of all non-negative real numbers. If f : R+ → R+ and g : R+ → R+ are defined as `f(x)=x^2` and `g(x)=+sqrtx` , find fog and gof. Are they equal functions ?


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

.


Find fog and gof  if : f (x) = x+1, g (x) = sin x .


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


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


Write the domain of the real function

`f (x) = sqrtx - [x] .`


Write the domain of the real function

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


Let A = {abcd} and f : A → A be given by f = {( a,b ),( b , d ),( c , a ) , ( d , c )} write `f^-1`. [NCERT EXEMPLAR]


Let\[A = \left\{ x \in R : - 1 \leq x \leq 1 \right\} = \text{B and C} = \left\{ x \in R : x \geq 0 \right\} and\]\[S = \left\{ \left( x, y \right) \in A \times B : x^2 + y^2 = 1 \right\} \text{and } S_0 = \left\{ \left( x, y \right) \in A \times C : x^2 + y^2 = 1 \right\}\]

Then,



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


If \[f : R \to R is given by f\left( x \right) = 3x - 5, then f^{- 1} \left( x \right)\] 

 


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


If the function

\[f : R \to R\]  be such that

\[f\left( x \right) = x - \left[ x \right]\] where [x] denotes the greatest integer less than or equal to x, then \[f^{- 1} \left( x \right)\]

 


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


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}


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

g(x) = |x|


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

h(x) = x|x|


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


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


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.

  • Let R: B → G be defined by R = { (b1,g1), (b2,g2),(b3,g1)}, then R 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 ____________.

If log102 = 0.3010.log103 = 0.4771 then the number of ciphers after decimal before a significant figure comes in `(5/3)^-100` is ______.


Number of integral values of x satisfying the inequality `(3/4)^(6x + 10 - x^2) < 27/64` is ______.


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


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 S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f: S `rightarrow` S such that f(m.n) = f(m).f(n) for every m, n ∈ S and m.n ∈ S is equal to ______.


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.


If f : R `rightarrow` R is defined by `f(x) = (2x - 7)/4`, show that f(x) is one-one and onto.


A function is called into if:


Which condition represents a many-one function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×