Find domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36

Step-by-step explanation:

Domain of Functions

Given a function h(x), we call the domain of h, all the values x can take so h exists. It's commonly easier to find the values of x for which h does NOT exist and then exclude them from the general domain of the real numbers.

The question provides us with the following functions

We called h(x) to the newly created function f/g(x)

To investigate the possible points of nonexistence for h, we factor h(x)

We can clearly see the denominator has two zeros at

A rational function cannot exist where the denominator is zero, regardless of the possible simplification with the numerator, as in this case. For example, for x=6 the function gets the value 0/0 and it's not defined there. We cannot simplify the common factor because they are part of the original function.

So, the domain of h is

Or equivalently

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.