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Math Help - Find Domain

  1. #1
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    Find Domain

    I have a hard time understanding how to find the domain of functions.

    Here are two samples:

    Find the domain of each function below.

    (a) u(h) = sqrt{h^2 - h - 2}

    (b) g(k) = k/(sqrt{k - 4})

    Must I rationalize the denominator for question (b) as a first step?

    What exactly is a DOMAIN anyway?

    How is it different from the range?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by blueridge View Post
    I have a hard time understanding how to find the domain of functions.

    Here are two samples:

    Find the domain of each function below.

    (a) u(h) = sqrt{h^2 - h - 2}

    (b) g(k) = k/(sqrt{k - 4})

    Must I rationalize the denominator for question (b) as a first step?

    What exactly is a DOMAIN anyway?

    How is it different from the range?
    the domain is the set of all input values for which a function is defined. in (a) it would be all values of h that work, and in (b) it is all values of k that work.

    to find the domain, it is usually easier to find values that don't work, and then say, the domain is all values but those values. if we have a fraction, we can't have the denominator being zero, so we say the domain is all values that don't make the denominator zero. for logs, what is being logged has to be greater than zero, so we say the domain is all values such that what is being logged is not less than or equal to zero. for square roots, what is being rooted has to be greater than or equal to zero, so the domain is all values that cause this to happen. of course there are conventions for stating the domain, the two most common ones are the set notation and the interval notation. tell me what values work for the two functions given and i will show you how to state it.

    for the range, this is the set of all outputs of a function, so for (a), it would be all u values we can get, and for (b) it would be all g values we can get from plugging in the values of the domain


    example. look at the function f(x) = y = x^2. what is the domain and range?

    the domain is all x, since we can plug in any x-value and get a y value. so we write, dom(f) = \left\{ x : x \in \mathbb { R } \right\} \mbox { or } dom(f) = ( - \infty, \infty)

    the range is given by : ran(f) = \left\{ y : y \geq 0, y \in \mathbb { R } \right\} \mbox { or } [0, \infty). why, becuase the graph does not show up for any other y values, we have no output that is negative
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  3. #3
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    sorry

    Sorry but you are using symbols unfamiliar to me.

    Can you explain in simple terms?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by blueridge View Post
    Sorry but you are using symbols unfamiliar to me.

    Can you explain in simple terms?
    none of the notations i used were familiar? the set notation may be weird, but i think you should have seen interval notation before.

    dom(f) is short for domain(f), f is the function, so "dom(f) = " is saying, "the domain of f is "

    the set notation is as follows. we enclose the set in { }. we begine by using a variable to represent the elements of the set. since i was talking about the domain, i was talking about the x-values (input values), so i began with, {x }

    we then insert a ":" or some people use "|", so {x : } is the same as {x | }

    what the ":" means is "such that". then we put a condition on the elements. so if i want all x > 0, i say dom(f) = {x : x > 0}, this means, "the domain of f is the set of x values such that the x's are greater than zero." now as good mathematicians, we have to know what kind of elements can we use, what set are we taking the elements from. should the x's be whoe numbers only, or real numbers or what? so then we use \in to mean "an element of the set" or "in"

    so to say x \in \mathbb { R } is to say, x is an element of the set of real numbers (we use \mathbb { R } to mean the set of real numbers)


    In any case, just tel me in english what are the domains and ranges for both functions, and i will walk you through how to write it properly in terms of math symbols
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