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Math Help - Find Domain of Function

  1. #1
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    Find Domain of Function

    Before answering the question for each function, I want to know if my defininition of domain and range is correct.

    Domain = the x-coordinate and Range = the y-coordinate, right?

    In other words, I can think of domain and range this way:

    (domain, range) = (x, y), right? If NOT, what is the CORRECT definition of domain and range in SIMPLE TERMS?

    QUESTIONS:

    Find the domain for each function below.

    (1) f(x) = x/(sqrt{x - 4})

    (2) q(x) = sqrt{x^2 - x - 2}

    Thanks!
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  2. #2
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    Quote Originally Posted by symmetry View Post
    Before answering the question for each function, I want to know if my defininition of domain and range is correct.

    Domain = the x-coordinate and Range = the y-coordinate, right?

    In other words, I can think of domain and range this way:

    (domain, range) = (x, y), right? If NOT, what is the CORRECT definition of domain and range in SIMPLE TERMS?

    QUESTIONS:

    Find the domain for each function below.

    (1) f(x) = x/(sqrt{x - 4})

    (2) q(x) = sqrt{x^2 - x - 2}

    Thanks!
    The domain is the set of all x for which T(x) is defined. If you have a digraph, it's all the values in the form x = ... that have a value y = ....

    "Domain = the x-coordinate"... almost.

    Range, on the other hand, is the set of all values in the form T(x) for some x in the domain of T.

    Similarly, in a digraph, there will be an x value for each y value.

    Are you familiar with onto and one-to-one?

    Now that you know what domain/range are, can you do these problems, or at least attempt them? If you show your thought process on these in the future, we can better help you find out where you're going wrong rather than just feeding you the answers...
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  3. #3
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    ok

    (1) f(x) = x/(sqrt{x - 4})...The domain would have to be x = 5 or greater. Yes?

    (2) q(x) = sqrt{x^2 - x - 2}...Domain would have to be all integers that do not produce the square root of a negative number, right?
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  4. #4
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    Quote Originally Posted by symmetry View Post
    (1) f(x) = x/(sqrt{x - 4})...The domain would have to be x = 5 or greater. Yes?

    (2) q(x) = sqrt{x^2 - x - 2}...Domain would have to be all integers that do not produce the square root of a negative number, right?
    1.) Almost!

    x > 4

    2.)

    When x = -1 and x = 2, y = 0.

    The graph is positive everywhere else, except between -1 and 2.

    Thus, there is a non-real result when:

    -1 < x < 2

    The domain, therefore, is all other values. Or, x >= 2 V x =< -1
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