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Thread: Help with a problem about operations on functions?

  1. #1
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    Help with a problem about operations on functions?

    Hello everyone. We were given homework on finding the domain and I managed to solve (a), (b), and (c) in the attached picture. On item number 5, it is asking me to get [(fg)∘h](4). I just wanted to know if there's a shortcut or an easier way to arrive at the answer? Because looking at f(x), g(x), and h(x), they all seem... a little too complicated.

    Thanks very much for your help!
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  2. #2
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    Re: Help with a problem about operations on functions?

    First, let me make sure I understand the notation used in your book:

    $$[(f\cdot g)\circ h](4) = (f\cdot g)(h(4)) = f(h(4))\cdot g(h(4))$$

    Is that correct? It seems pretty straightforward to me. Just plug it in. I get a final answer of 3.
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  3. #3
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    Re: Help with a problem about operations on functions?

    You are given that $\displaystyle h(x)= \frac{\sqrt{x}- 2}{x^2- 9x- 10}$. So what is y= h(4)? Then $\displaystyle f(y)= \frac{y^2+ 4}{\sqrt{y+ 4}}$ and $\displaystyle g(y)= \sqrt{|y- 15|- 6}$. What are those for y= h(4)? What is their product?
    Last edited by HallsofIvy; Sep 20th 2018 at 09:28 AM.
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    Re: Help with a problem about operations on functions?

    Quote Originally Posted by HallsofIvy View Post
    Shtuff!
    Oops, my mistake. That's what I get for trying to do mental math during a meeting :-P. 3 is not correct. Use what Hallsofivy is showing. It will get the correct answer.
    Last edited by SlipEternal; Sep 20th 2018 at 09:41 AM.
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    Re: Help with a problem about operations on functions?

    Too fast! I had decided that I shouldn't give the complete solution so edited to just say what should be done- but now it is here forever!
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    Re: Help with a problem about operations on functions?

    Quote Originally Posted by HallsofIvy View Post
    Too fast! I had decided that I shouldn't give the complete solution so edited to just say what should be done- but now it is here forever!
    Fixed it
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    Re: Help with a problem about operations on functions?

    Quote Originally Posted by HallsofIvy View Post
    Too fast! I had decided that I shouldn't give the complete solution so edited to just say what should be done- but now it is here forever!
    I'll remove it for you. I accept cash, money orders, and traveler's checks. I don't trust the people at PayPal.

    The cost is my usual bribe amount. Take a chessboard, put one penny on the first square, two on the second, four on the third, eight on the next, and so on. I want all the money on the chessboard.

    I accept payment plans with a minimal amount of compound interest.

    -Dan
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  8. #8
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    Re: Help with a problem about operations on functions?

    Unfortunately, I can't find my chess board! I found an old checkerboard but of course that wouldn't be good enough.
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    Re: Help with a problem about operations on functions?

    Quote Originally Posted by HallsofIvy View Post
    Unfortunately, I can't find my chess board! I found an old checkerboard but of course that wouldn't be good enough.
    I love doing that to my students. They say, "Hey, it's only a couple hundred of dollars." Then I tell them to calculate the last square and compare it with the national deficit.

    -Dan
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    Re: Help with a problem about operations on functions?

    Quote Originally Posted by topsquark View Post
    I love doing that to my students. They say, "Hey, it's only a couple hundred of dollars." Then I tell them to calculate the last square and compare it with the national deficit.

    -Dan
    I play chess online. I can write a program that would put pennies on a chess board, but a bunch of pixels won't be worth much.
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  11. #11
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    Re: Help with a problem about operations on functions?

    Thank you everyone! I finally get it now.
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