You just reminded me that I need to start focusing on my third year finance (Since intro finance can be a joke somewhat), namely the pricing of put and call options.

Stop being lazy and do your own homework

My calculus is a little rusty (haven't taken it in years)

But I think I can help you out with the second one.

Remember f(x) is basically y (think axis)

first thing you want to do is zero out the equation in the square root because nothing in a square root is allowed to be negative

so it will look like this    0=-2x-4

then solve for x 

4 = -2x which is x= -2   that's half the answer.

Remember: nothing in a square root can be negative.

if you replace x with -2, inside the square would be 0, the tipping point between positive and negative. so we're on the right path.

so we know the domain either starts or ends at -2

now lets see what happens if we put -1 or negative -3 to see where the inside of the square root stays positive,and if the domain heads to the more negative side or positive.  

if we put -1 (which is going towards positive infinity), inside the square root will be  -2 !! But we want the inside of the square root to remain positive so we know it's not going towards positive infinty.

Lets replace x with -3. What is the inside of the root equal to now? it equals 2 Bingo!

so the ending point is -2 when we zero out the root.

if we replace x with numbers that are heading torwards negative infinity, the inside of the square root remains positive.

So the domain is (-infinity, -2) 

I've gone up to matrix shit and linear algebra, but I'm so done with math there's no way I'm going to do this.

Have fun Soriku. <3 The least I can do is bump this for you.

Maybe if you had FUN Calculus questions I would answer. But no. You have aggravating crap. =P

wow, a simple thanks would have been more than enough ...

I fixed the -2 like ten minutes ago

and ( means it can never actually equal - infinity but it's close to it

[ means it can be the actual number (-2) and still be a correct function

Yeah, I should have mention the brackets in the answer (-infinity, -2] ... like I said, it's been years. 

It's moments like these where I start realizing how emotionless internet people are.

Nevermind. It's been explained.

?????

I suck ass at math, ever since I had a teacher who decided giving us test questions on things we hadn't covered yet was a good idea. After reading that answer I suppose it wouldn't be insanely difficult for me to get the hang of, but I honestly will never have a use for calculus I don't think.

h(x *1/b) will casue a horizontal dilation with a scale factor of 1/1.6

It will scale up (widen) because |1.6| >1

That answers the second part of your question.

The first section of your question, you just simply replace x with x/1.6 in your initial function.

Edit: Let me know if more explanation is needed. I do apologize if it is unclear or even wrong (!). It's 3:30AM here and it's been a mess since hurricane Igor had hit. Still trying to straighten things.

Edit 2: I can't believe the bad-mouthing math is getting. I teach it for a living, I will not stand for this!

Good try, but you're not looking for a solution. You're re-writing the equation so that it measures in kilometres.

What the question is, is simply presenting you with a basic transformation. The complicated equation is only a distraction. When you have a transformation of form f(x) -> f(1/b *x) you have a dilation or a change of scale - widen or shorten horizontally.

Try a more simple example on your calculator to illustrate the point:  Y1 = x^2    and    Y2= (x/1.6)^2  See when b>1 it widens.

See how that same transformation works on a simple function? The same behaviour will occur with the transformation on your question. You should probably have some notes on transformations - check them over too!

I'm unsure if your teacher wants anything done with the 10 < x < 100 part.

Yeah, I teach math. Typically junior high, though. Haven't had much opportunity with high school maths yet besides general/basic courses.