IIT JEE , AIEEE Forum - Mathematics , Algebra

aman.dhanda

I want to know the different methods of finding domain and range for different questions.

Plzzzzzzz help me!!!

aditya.thakar

A={1,2,3}

B={4,5,6}

A*B={(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)}

than Domain={1,2,3} and Range={4,5,6} so Domain is equal to first element of each pair and Range is equal to second element of each pair......

aman.dhanda

I want the methods to find domains and range of equations containing roots, logarithm, quadratic equations etc like:-
f(x)=2x^2+2x+1/x^2+4x+3

aditya.thakar

its simple if x belongs to N take x=1 and wat u wil get is velue of y so u got one pair than take x=2,3,4,........ and u wil get y for each velue and than make pairs and the first element of each pair is Domain and second element of each pair is Range. i wil give u the answer but actually i dont know wat is this ^ ?

khinart

Domain: Domain of y = f(x) is set all real x for which f(x) is defined (real).

How to find Domain:

(i) Expression under even root (i.e. square root, 4th root) 0

(ii) Denominator 0

(iii) If domain of y = (x) & y = y(x) are D1 & D2 respectivly then domain of f(x) ± y(x) of f(x).g(x) is D1 D2.

(iv) Domain of is D1 D2 - {g(x) = 0}.

khinart

Range: Range of y = f(x) is collection of all output & {F(x)} corresponding to each real no. is domain.

How to find range:

First of all final domain of y = f(x)

(i) If domain Finite no. of points range set of corresponding f(x)values.

(ii) If domain R or R - {some finite points}
Then express x in terms of y. From this find y for x to be defined. (i.e. find values of y for which x exists)

(iii) If domain a finite interval, find least and greatest value for range using mono tonicity.

khinart

See these are the standard methods for finding the range and domain of the function.Please the most important tip for finding the domain and the range is that U MUST FIRST CONVERT THE FUNCTION INTO SIMPLEST FORM SO THAT U KNOW THE VALUES int which the function oscillates.

Cheers!!!!!!!!!!!!!!!!!!!

aditya.thakar

f(x)=2x^2+2x+1/x^2+4x+3 if x belongs to N numbers

f(1)=5/8

f(2)=13/15

f(3)=25/24

.

so domain of f Df={1,2,3,.......}

and Rf={5/8,13/15,25/24,.........}

if i m right than rate me for my effort and wrong than tell me where m wrong?

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