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Math Help - Domain and Range of Function: f(x)=1/x^2-9

  1. #1
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    Domain and Range of Function: f(x)=1/x^2-9

    Considering the last thread was so incredibly helpful I decided to post yet again. Sorry for creating another thread!

    I have the equation: f(x)=1/x^2-9 written in my textbook and the question states "find the domain and range of f(x)"

    I have never seen something similar to this and was wondering how I'm meant to work out the domain and range or find it withing the equation? is there a specific formula for finding it?

    Also, how are we able to tell if f(x) is even, odd or neither?

    Cheers,
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  2. #2
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    Quote Originally Posted by jnow2 View Post
    Considering the last thread was so incredibly helpful I decided to post yet again. Sorry for creating another thread!

    I have the equation: f(x)=1/x^2-9 written in my textbook and the question states "find the domain and range of f(x)"

    I have never seen something similar to this and was wondering how I'm meant to work out the domain and range or find it withing the equation? is there a specific formula for finding it?

    Also, how are we able to tell if f(x) is even, odd or neither?

    Cheers,
    Is it 1/(x^2) - 9 or 1/(x^2 - 9)?
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  3. #3
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    1/(x^2 - 9)

    there's actually no brackets in the equation at all. but i'd say its more likely this one as opposed to the other.
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    Quote Originally Posted by jnow2 View Post
    1/(x^2 - 9)

    there's actually no brackets in the equation at all. but i'd say its more likely this one as opposed to the other.
    Well that's because the question was typeset from where you got it from, like this: \frac{1 }{x^2 - 9}

    and so there's obviously no ambiguity. But what you typed, 1/x^2 - 9, is not typeset properly and there's an obvious ambiguity in how to interpret it, which I pointed out.

    The domain is all real numbers except those such that x^2 - 9 = 0. The range is best found by drawing a graph, and is \{y: \, -\infty < y \leq -1/9 \} \cup \{y: 0 < y < +\infty \}.
    Last edited by mr fantastic; March 30th 2010 at 02:08 AM. Reason: Corrected a typo
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    Quote Originally Posted by mr fantastic View Post

    The domain is all real numbers except those such that x^2 - 9 = 0. The range is best found by drawing a graph, and is \{y: \, -\infty < y \leq -9 \} \cup \{y: 0 < y < +\infty \}.
    What does the U in that last section mean?
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    Quote Originally Posted by jnow2 View Post
    What does the U in that last section mean?
    Union.

    Quote Originally Posted by jnow2 View Post
    [snip]
    Also, how are we able to tell if f(x) is even, odd or neither?

    Cheers,
    Even: f(-x) = f(x)

    Odd: f(-x) = - f(x)

    Neither: None of the above.
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  7. #7
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    oops, sorry! should have read forum rules first!

    I'm still attempting to calculate the domain and range for f(x) in the equation
    f(x)= 1/ (x^2-9).

    Many of my friends have been saying that the domain is written as :
    "all real x, x not equal to 3 and -3" and "y=all real y, y not equal to 0" but I still have no idea how they get the domain and range (and if they're right) and what these tell us about the equation!
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  8. #8
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    Quote Originally Posted by jnow2 View Post
    oops, sorry! should have read forum rules first!

    I'm still attempting to calculate the domain and range for f(x) in the equation
    f(x)= 1/ (x^2-9).

    Many of my friends have been saying that the domain is written as :
    "all real x, x not equal to 3 and -3" and "y=all real y, y not equal to 0" but I still have no idea how they get the domain and range (and if they're right) and what these tell us about the equation!
    Post #4 tells you how to get the domain, can you solve the equation I gave you?

    The range found by your friends is wrong - post #4 tells you how to get it (note: I corrected a typo). To draw the graph, you should consider the reciprocal of the simple graph y = x^2 - 9 ....
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