# Thread: A few Calculus problems.

1. ## 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!

2. Originally Posted by mcra7x
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

3. 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 ?

4. 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!

5. Originally Posted by mcra7x
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...."