हिंदी

Let = Sin X. If F is a Bijection, Write Set A.

Advertisements
Advertisements

प्रश्न

Let \[f : \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right] \to\] A be defined by f(x) = sin x. If f is a bijection, write set A.

Advertisements

उत्तर

\[\because\]  f is a bijection, 

co -domain of f = range of f 

As  \[- 1 \leq \sin x \leq 1\]

\[- 1 \leq y \leq 1\]

So, A = [-1 , 1]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Functions - Exercise 2.5 [पृष्ठ ७३]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 2 Functions
Exercise 2.5 | Q 20 | पृष्ठ ७३

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Let A = {−1, 0, 1} and f = {(x, x2) : 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) = x2 + x


Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = x3 + 1


Show that the logarithmic function  f : R0+ → R   given  by f (x)  loga x ,a> 0   is   a  bijection.


Show that f : R→ R, given by f(x) = x — [x], is neither one-one nor onto.


Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.


Let f be a real function given by f (x)=`sqrt (x-2)`
Find each of the following:

(i) fof
(ii) fofof
(iii) (fofof) (38)
(iv) f2

Also, show that fof ≠ `f^2` .


Show that the function f : Q → Q, defined by f(x) = 3x + 5, is invertible. Also, find f−1


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.


Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x3. Write f−1(1).


If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).


Let A = {x ∈ R : −4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\]Write the range of f.


If f : R → R be defined by f(x) = (3 − x3)1/3, then find fof (x).


If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then find fog.    [NCERT EXEMPLAR]


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


Let

\[f : R \to R\]
\[f\left( x \right) = \frac{x^2 - 8}{x^2 + 2}\]
Then,  f is


A function f from the set of natural numbers to the set of integers defined by

\[f\left( n \right)\begin{cases}\frac{n - 1}{2}, & \text{when n is odd} \\ - \frac{n}{2}, & \text{when n is even}\end{cases}\]

 


\[f : Z \to Z\]  be given by

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

Then,  f is


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


Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.


Mark the correct alternative in the following question:

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

 

 


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

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


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

g(x) = |x|


If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is ______.


The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is ____________.


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


If N be the set of all-natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is ____________.


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


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. Based on the given information, f is best defined as:


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: R → R be defined by f(x) = x2 is:

Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if  "n is even"):}` Is the function injective? Justify your answer.


If f: R→R is a function defined by f(x) = `[x - 1]cos((2x - 1)/2)π`, where [ ] denotes the greatest integer function, then f is ______.


A function is onto when every element of the codomain has:


For \(f(x)=x^2+x\), if \(y=1\), which two domain elements have the same image?


Which real-life situation resembles a one-one idea when no roll number is repeated?


Which condition represents a one-one (injective) function?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×