Results 1 to 5 of 5

Thread: A few Calculus problems.

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    2

    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!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    5
    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 $\displaystyle (1, \infty)$. 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 $\displaystyle f^{-1}(10) = x$, then we have $\displaystyle 10 = f(x)$

    now, can you say what $\displaystyle f^{-1}(10)$ 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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    2
    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 ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1
    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 $\displaystyle f^{-1}(10)$ 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. $\displaystyle f^{-1} (10)$ 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!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    5
    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 $\displaystyle f^{-1}(10) = x$ is the same as saying $\displaystyle f(x) = 10$. 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 $\displaystyle \ln (\ln x)$ is all real $\displaystyle x$ so that $\displaystyle \ln x > 0$. $\displaystyle \ln x = 0$ for $\displaystyle x = 1$, thus we want $\displaystyle x > 1$

    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...."
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Jun 25th 2010, 10:41 PM
  2. 3 problems from Calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 26th 2009, 08:14 AM
  3. 2 calculus problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Mar 3rd 2008, 07:48 AM
  4. Min/Max Calculus Problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jan 9th 2007, 04:34 PM
  5. 3 Calculus Problems
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Jan 8th 2007, 04:16 AM

Search Tags


/mathhelpforum @mathhelpforum