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Math Help - domain

  1. #1
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    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.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wutever View Post
    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
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  3. #3
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    thx for the reply but wut abt the sin and cos ones ?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wutever View Post
    thx for the reply but wut abt the sin and cos ones ?
    Quote Originally Posted by wutever View Post
    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
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