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find the domain and range of following function-

this Q.are in r.d sharma.plz.fast ans.

THANK,YOU

^{-1}x + cosec^{-1}xlog

_{4}(2log_{3}( 1 + log_{2}( 1 + 3log_{3}x))) = 1/2. Find x.If the function f : R --- R defined by f(x) = x

^{2}+ 5x + 9 find f^{-1}(9)(Right answers will definitely get thumbs up (only for students) - urgent)

Let f: N -- R de function defined as f(x) = 4x

^{2 }+ 12x +15. Show that f : N-- S, where S is the range of f is invertible. Find f^{-1 }.Given the relation R={(1,2)(2,3)} on set A={1,2,3} add a minimum number of order pair so that enlarged relation is symmetric ,transitive an d reflexive.

_{2}log_{1/2}log_{3}x > 0.............. plzz explain the steps as well..find the range of f(x) = under root 16-x

^{2}what is the range of the function f(x)=square root of 3x

^{2}-4x+5?for all positive integers n let f(n)= log 2002 n^2 .LET N =f(11)+ f(13)+ f(14)

which of these relations is true? why

find the range of the function

f(x) = 3sinx + 4cosx - 5

^{-1}( (2x+1) / (2(2x)^{1/2}) ) ._{3}(5 + 4x - x^{2}) .^{2}- x]) / (1 + sin(cos x)) .let f be one one function with domain {x,y,z} and range {1,2,3}.it is given that exactly one of the following statement is true and remaining two are false.

f(x)=1,f(y)not equal to 1,f(z) not equal to 2.determine f inverse(1)

f(x) = log

_{21/2}(2-log_{2}(16sin^{2}x+1)) : Find the range of the functionA small ring of radius r rolls without slipping in side a fixed hollow cylinder of radius R with small oscillations about stable equilibrium as shown in the fig. The frequency of oscillation is ?

a.1/2ÐŸ (g/R-r)

^{0.5}b.1/2ÐŸ(2g/R-r)^{0.5}c.1/2ÐŸ(3g/2(R-r))^{0.5}d.1/2ÐŸ(g/2(R-r))^{0.5}Determine whether each of the following relations are reflexive, symmetric and transitive:

(i)Relation R in the set

A= {1, 2, 3…13, 14} defined asR = {(

x,y): 3x−y= 0}(ii) Relation R in the set

Nof natural numbers defined asR = {(

x,y):y=x+ 5 andx< 4}(iii) Relation R in the set

A= {1, 2, 3, 4, 5, 6} asR = {(

x,y):yis divisible byx}(iv) Relation R in the set

Zof all integers defined asR = {(

x,y):x−yis as integer}(v) Relation R in the set

Aof human beings in a town at a particular time given by(a) R = {(

x,y):xandywork at the same place}(b) R = {(

x,y):xandylive in the same locality}(c) R = {(

x,y):xis exactly 7 cm taller thany}(d) R = {(

x,y):xis wife ofy}(e) R = {(

x,y):xis father ofy}If 3f(x)+5f(1/x)=1/x -3,then f(x) =

(a)1/14(3/x +5x -6) (b)1/14(-3/x +5x -6) c)1/14(-3/x +5x+6) d) none of these

^{3}-12x is ? (a)[8, 72] (b)[-8, 72] (c)[0,8] (d)none{ANSWER IS [-8, 72]}

^{-1}[2x^{2}-3](A) f(x+2) = f(x-2) (B) f(2+x) = f(2-x) (C) f(x) = f(-x) (D) f(x) = (- f(-x))

IF F( X) IS A POLYNOMIAL FUNCTION SATISFYING F(X)*F(1/X)=F(X) + F(1/X),AND F(3)=28 ,THEN F(4) IS EQUAL TOA.63

B.65

C.68

D.67

Find domain of (3x)/(28-x)

Please explain this question

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y⊆X, Z⊆X and Y∩Z is empty, is

Find range of 3/(2-x

^{2})Q) f: R--- R is a function satisfying f(2x+3) + f(2x+7) = 2 ( x belong to R) , then period of f(x):

(ans:4)

^{2}+3 Find1. {x:f(x)=28} 2. The pre images of 39 and 2 under 'f '

find the value of the ratios, sin 3060

1 {2,4,8}

2{2,4,6,8}

3{2,4,6}

4{1,2,3,4}

Check whether the relation R inRdefined as R = {(a,b):a≤b

^{2}}find the range of f(x) = 3/ 2-x

^{2}Please explain this in simple manner.

a. (1/2,2)

b. (4/3,2)

c.(0,2)

d. (0,4/3)

Domain of root a

^{2}- x^{2}(a 0)^{2}) + log_{10}(x^{3}- x) what is the domain of the function2.if f(x) = cos[pie

^{2}]x + cos[-pie^{2}]x, where [x] stands for the greatest integer function ,thenopt.1.f (pie/2)=-1 2.f (pie)=1 3.f (-pie)=0 4.f (pie/4)=1 i want solution of these questions

^{2}+6x-5, show that f is invertible with f^{-1}(y)=(y+6)^{1/2}-1/3.How to find range of a function ?

Find the number of all onto functions from the set {1, 2, 3, … ,

n) to itself.f: A→ B defined by. Show thatfis one - one and onto and hence, findf.^{-1}how to find the period of a function?

let f be continuous function on [1,3]. If f takes only rational values for all x and f(2)=1- , find f(1.5)

plzgive the ans tof my question !!!!

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(

x,y): 3x–y= 0, wherex,y∈ A}. Write down its domain, codomain and range.f(x) = log(x+√(x

^{2}+1) isa. an odd function

b.a periodic function

c. an even function

d. none of these

Please explain brieflyLet f : R-R defined by f(x) = x

^{3}+ ax^{2}+ 3x + 100. Then find the value of 'a' for which f is one one function.Pls explain me this question in words particulrly as i can understand the steps but not why is it used

if X = {4

^{n}3n 1 :n∈ N} and Y = {9(n 1) :n∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to:If f (x) is a polynomial function satisfying 2 + f (x) f (y) = f (x) + f (y) +f (xy) , for all x,y belong to R and f (2) =5.

Find the value of f (f (2)).

Q.write the range of the function f(x)=sin[x],where x belongs to[-pi/4,pi/4].

Q.write the range of function f(x)=cos[x],where x belongs to (-pi/2,pi/2).

Q.write the range of the function f(x)=e^(x-[x] ),x may be real num.

If f(x) = x

^{3}+ 3x^{2}+ 12x - 2sinx ,where f: R-R,thenThe real x and y satisfying simultaneously log

_{8}x + log_{4}y^{2}= 5log_{8}y + log_{4}x^{2}= 7, then the value of xy equal to -(A) 2^{9}(B) 2^{12}(C) 2^{18}(D) 2^{24}If f :R-R, where f(x) = ax + cosx and f(x) is bijective, then

^{+}^{-}the domain of the function f(x)=square root of x

^{2}-5x+6 + square root of 2x+8-x^{2}a) [2,3]

b) [-2,4]

c) [-2,2] U [3,4]

d) [-2,1] U [2,4]

^{-1}[(x+3)x]^{1/2}+ cos^{-1}[x^{2}+3x+1]^{1/2}is defined on the set S , where S equal to(A) {0 , 3} (B) (0 ,3) (C) {0, -3} (D) [-3, 0]

Write the following in set builder form

{...-4,-3,-2,-1,0,1,2,3,4..}

find the range of 1/1-x2

Find the range of f(x)=cos[x],for x lies between -pi/2 to pi/2Thanks for giving answer to my query but Iwould like to inform that I am not able to understand the solution pls explain it in detailsolution given by you earlierThe given function is f(x)=cos[x],for -pi/2Since the angle is [x] so the interval -pi/2 1. -pi/2 2. -1 3. 0 4. 1 In the interval -pi/2 So, cos [x] = cos(-2) = cos 2In the interval -1 So, cos [x] = cos(-1) = cos 1In the interval 0 So, cos [x] = cos0 = 1In the interval 1 So, cos [x] = cos1Thus, the range of f(x) = cos[x], for -pi/2

find the range of f(x) = 1/ under root x-5

<f(2); f(3)>f(4) and f(5)=5 which of the following is true-Will fo(g + h) = (fog) + (foh)

F(X)= underrroot(X

^{2 }- 4X +6)If a set A has 10 elements and set B has 5 elements what is the number of injective, surgetive and bijective functions from A to B

R ={(x,y): x+2y

Find domain and range.

let f(x)=x

^{3}+3x2-33x-33 for x0 and g be its inverse ,then the value of k such that g'(2)=1 is equal to1.72 2.-42 3.124.none of these

are greatest integer function and step up function same thing or different thing.If same then please explain all proofs of greatest integer function's properties and if different then whats the difference between them?

A person spends 40% of his salary on food and 30% on rent. If he

savesRs 6000 per month what is his monthly salary?

x∈ N* (–2, δ) ⇒f(x) ∈ (8.99, 9.01), then the maximum value of δ is ................ wheref(x) –5 – 2x.(a) 0.005 (b) 0.009 (c) 0.001 (d) None of these

a regular octagon is formed by cutting congruent isoceles traingles from the corners of a square,if the square has side length 1 the side length of the octagon is?

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