# Thread: Two questions on where to start

1. ## Two questions on where to start

Hi, I am stuck on where to begin with the following questions:

and

For the first image I get a and b. I get a because it is in my textbook as an example proof, but don't fully understand why. I get b because I can relate to it with simple physics. However, c and d are the same questions and I do not understand what it is referring to. How can you solve for x when 0<a<b and 0<b<a. I don't understand what they are trying to say with the variables of a & b. I know this is early calculus and I should know this, but in high school I was not taught mathematical theory, but was taught everything on how to calculate answers.

For the second image, I don't even know what f(x) is even saying. My calculus professor never told the class what it is meant by the mathematical writing it has. As well, I don't understand what it means that f(x) is periodic but as no period. To me, I don't see how that is possible.

I attempted this with a friend today that is in the same class. She had no idea what to do as well. We both didn't even know where to start. Where to even begin is what I am really asking for help on.

2. ## Re: Two questions on where to start

it is helpful the think of the quantity |x-a| as "the distance between x and a".

so |x-a| < |x-b| means "x is closer to a than it is to b". for which real numbers can this be true for, given that a < b?

for example, if a = 3, and b = 5, then |x - 3| < |x - 5| means x is closer to 3 than it is to 5. this is true for 3.5, it is not true for 6. can you generalize?

for the second problem, a function f is periodic if there exists a number a such that f(x) = f(x + ka) for any integer k, and for all x.

clearly the function shown repeats every 1/2, every 1/3, every 1/4, etc.....is there a smallest such period?