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Math Help - A few Calculus problems.

  1. #1
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    A few Calculus problems.

    I have been working on my AP Calculus homework, and there are a few things I can't understand. Can you help? These are three, seperate, unrelated problems.

    1) I need to graph and explain the graph of ln(ln(x))

    2) For the graph of the function of f, where x = # of DVDs produced and y = Cost of production, what does f^-1(10) represent? (That's f-inverse(10), I wasn't sure if the way I typed it was correct or not.)

    3) I was given the inverse function of F. Do I get F using the same method I would to get inverse of F only go the other way around? and is finding the F function how I should be finding f(1)?

    If anybody helps, I really appreciate it. And I'm not specifically looking for answers, I would like an explanation of how to do the problems. I like knowing how and why instead of what the answer is. Thanks again!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mcra7x View Post
    I have been working on my AP Calculus homework, and there are a few things I can't understand. Can you help? These are three, seperate, unrelated problems.

    1) I need to graph and explain the graph of ln(ln(x))
    so what have you done here? note that the domain of the graph would be (1, \infty). why? and it will be in a somewhat similar in shape to ln(x) but it would increase less steeply. why?

    2) For the graph of the function of f, where x = # of DVDs produced and y = f(x) = Cost of production, what does f^-1(10) represent? (That's f-inverse(10), I wasn't sure if the way I typed it was correct or not.)
    do you understand the relationship between a function and its inverse?

    say f^{-1}(10) = x, then we have 10 = f(x)

    now, can you say what f^{-1}(10) was?

    3) I was given the inverse function of F. Do I get F using the same method I would to get inverse of F only go the other way around?
    yes

    and is finding the F function how I should be finding f(1)?
    after you find f, plug in 1
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  3. #3
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    I still do not understand #2. I am not needing to know the value of f^-1(10) but what it represents.

    How did you find the domain of number one? I thought the domain of ln was [0, infinity)

    And how are you doing those math symbols? That's pretty cool.

    The inverse of a function is a reflection over the line y=x ?
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  4. #4
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    I have been working on my AP Calculus homework, and there are a few things I can't understand. Can you help? These are three, seperate, unrelated problems.

    1) I need to graph and explain the graph of ln(ln(x))

    Have you graphed it? Remember that it is not saying ln(x) times ln(x), this is a composite function, ie. f(g(x)) so you are evaluating ln(x) IN TERMS OF ln(x). This is a really cool question and I think if you look at the graph of this function for awhile you can come up with a good answer. Hint: Remember that a log is just an exponent. These kinds of questions are supposed to make you think, not get an answer from someone on a help forum. If you are in AP Calculus, you didn't get there by accident

    2) For the graph of the function of f, where x = # of DVDs produced and y = Cost of production, what does f^{-1}(10) represent?

    Typically, the inverse of a cost vs. production graph, is the price per unit of what ever is being produced. Cost of production increases as more units must be produced; the more units they can sell means the lower the price of each unit can be. f^{-1} (10) is asking you what is happening on the inverse graph of f(x) at x=10.

    3) I was given the inverse function of F. Do I get F using the same method I would to get inverse of F only go the other way around? and is finding the F function how I should be finding f(1)?

    If f is the inverse of g, then g is the inverse of f. This is an elementary property of inverse functions.

    If anybody helps, I really appreciate it. And I'm not specifically looking for answers, I would like an explanation of how to do the problems. I like knowing how and why instead of what the answer is. Thanks again!
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mcra7x View Post
    I still do not understand #2. I am not needing to know the value of f^-1(10) but what it represents.
    f(x) is the cost, x is the number of DVDs. i told you that saying f^{-1}(10) = x is the same as saying f(x) = 10. now can you state what it represents?

    How did you find the domain of number one? I thought the domain of ln was [0, infinity)
    actually, zero is not included in the domain

    thus, the domain of \ln (\ln x) is all real x so that \ln x > 0. \ln x = 0 for x = 1, thus we want x > 1

    And how are you doing those math symbols? That's pretty cool.
    see here.

    The inverse of a function is a reflection over the line y=x ?
    that's true. but that's not the relationship i was going for. Molly already said it, "if f is the inverse of g, then g is the inverse of f...."
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