# Thread: domain

1. ## domain

hey, here is the question:
find the natural domain of these functions:-
1.) f(x)= 1/(1-sinx)
2.) f(x)= x/|x|
3.) f(x)= √(x^2-4)/(x-4)
4.) f(x)= (x^2-1)/(x+1)
5.) f(x)= 3/(2-cosx)
6.) f(x)= 3+ √x
7.) f(x)= x^3 +2
8.) f(x)= 3 sin x
9.) f(x)= 3/x
10.) f(x)= sin^2 √x

thx in advance.

2. Originally Posted by wutever
hey, here is the question:
find the natural domain of these functions:-
1.) f(x)= 1/(1-sinx)
2.) f(x)= x/|x|
3.) f(x)= √(x^2-4)/(x-4)
4.) f(x)= (x^2-1)/(x+1)
5.) f(x)= 3/(2-cosx)
6.) f(x)= 3+ √x
7.) f(x)= x^3 +2
8.) f(x)= 3 sin x
9.) f(x)= 3/x
10.) f(x)= sin^2 √x

thx in advance.
Ask yourself the question: "Is there any place where the function does not exist?" Then take those values of x away from the real line and there's your answer.

For example:
$f(x) = \frac{x}{|x|}$
does not exist when x = 0 because a zero in the denominator is not defined. Thus the domain is $(-\infty, 0) \cup (0, \infty)$ (otherwise known as "all real numbers, except x = 0.")

-Dan

3. thx for the reply but wut abt the sin and cos ones ?

4. Originally Posted by wutever
thx for the reply but wut abt the sin and cos ones ?
Originally Posted by wutever
hey, here is the question:
find the natural domain of these functions:-
1.) f(x)= 1/(1-sinx)
5.) f(x)= 3/(2-cosx)
8.) f(x)= 3 sin x
10.) f(x)= sin^2 √x

thx in advance.
What about them? Is there any restriction on x if f(x) = sin(x)? or f(x) = cos(x)? Note there will be restrictions for 1 and 5 since the denominator cannot be 0. (Well, there isn't a restriction on 5, see if you can figure out why.) And the restriction in 10 has nothing to do with the sine function.

-Dan

### domain of 1/(1-2cosx)

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