मराठी

Let D be the domain of the real valued function f defined by f(x) = 25-x2. Then, write D - Mathematics

Advertisements
Advertisements

प्रश्न

Let D be the domain of the real valued function f defined by f(x) = `sqrt(25 - x^2)`. Then, write D

बेरीज
Advertisements

उत्तर

Given real valued function f(x), such that f(x) = `sqrt(25 - x^2)`

Since  f(x) is reaal valued

We must have

25 – x2 ≥ 0

⇒ x2 ≤ 25

⇒ – 5 ≤ x ≤ 5

⇒ The Domain D = [–5, 5]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Exercise [पृष्ठ ११]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 1 Relations And Functions
Exercise | Q 2 | पृष्ठ ११

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

Show that the function f : R* → R* defined by f(x) = `1/x` is one-one and onto, where R* is the set of all non-zero real numbers. Is the result true if the domain R* is replaced by N, with the co-domain being the same as R?


Show that the Signum Function f : R → R, given by `f(x) = {(1", if"  x > 0), (0", if"  x  = 0), (-1", if"  x < 0):}` is neither one-one nor onto.


Let f : R → R be defined as f(x) = x4. Choose the correct answer.


Show that the function f : R → {x ∈ R : −1 < x < 1} defined by f(x) = `x/(1 + |x|)`, x ∈ R is one-one and onto function.


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

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


Give an example of a function which is one-one but not onto ?


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

f3 = {(ax), (bx), (cz), (dz)} ; A = {abcd,}, B = {xyz}. 


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.


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


Consider f : N → Ng : N → N and h : N → R defined as f(x) = 2xg(y) = 3y + 4 and h(z) = sin z for all xyz ∈ N. Show that ho (gof) = (hogof.


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


Let f : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]


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 A = {1, 2, 3, 4} and B = {ab} be two sets. Write the total number of onto functions from A to B.


Write the domain of the real function

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


Let f : R → R be the function defined by f(x) = 4x − 3 for all x ∈ R Then write f .   [NCERT EXEMPLAR]


\[f : Z \to Z\]  be given by

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

Then,  f is


Let  \[f\left( x \right) = x^2 and g\left( x \right) = 2^x\] Then, the solution set of the equation

\[fog \left( x \right) = gof \left( x \right)\] is 



Let

 \[A = \left\{ x \in R : x \geq 1 \right\}\] The inverse of the function, 

\[f : A \to A\] given by

\[f\left( x \right) = 2^{x \left( x - 1 \right)} , is\]

 


Let  \[f\left( x \right) = \frac{1}{1 - x} . \text{Then}, \left\{ f o \left( fof \right) \right\} \left( x \right)\]

 


 Let
\[g\left( x \right) = 1 + x - \left[ x \right] \text{and} f\left( x \right) = \begin{cases}- 1, & x < 0 \\ 0, & x = 0, \\ 1, & x > 0\end{cases}\] where [x] denotes the greatest integer less than or equal to x. Then for all \[x, f \left( g \left( x \right) \right)\] is equal to


Let N be the set of natural numbers and the function f: N → N be defined by f(n) = 2n + 3 ∀ n ∈ N. Then f is ______.


Let C be the set of complex numbers. Prove that the mapping f: C → R given by f(z) = |z|, ∀ z ∈ C, is neither one-one nor onto.


Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections from A into B is ______.


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


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


Range of `"f"("x") = sqrt((1 - "cos x") sqrt ((1 - "cos x")sqrt ((1 - "cos x")....infty))`


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?

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 ____________.

Let f: R → R defined by f(x) = x4. Choose the correct answer


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


The domain of the function `cos^-1((2sin^-1(1/(4x^2-1)))/π)` is ______.


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



The given function f : R → R is not ‘onto’ function. Give reason.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×