Answer:
When we have a random function like:
y = f(x)
If there is no clarification, the domain will be the set of all real numbers except the ones that may make a problem.
For example, if there is some value of x such that there is a denominator equal to zero, then that particular value of x is not in the domain of f(x) (because we can not divide by x)
Something similar happens when we have a square root, remember that:
√x
Is a complex number if x < 0.
Then if we have a function like:
y = √x
The domain will be the set of all reals such that x ≥ 0.
Then the procedure to find the domain is to find the inputs that may have problems, and "remove" them from the domain.
For the range, we need to first know the domain, then we can evaluate the function in different points of the domain and see the outputs. Once we know all the outputs, we know the range of the function.
Usually, when working with continuous functions, these may have a global maximum M and a global minimum m, then the range is:
m ≤ Y ≤ M
if not, then the range is the set of all real numbers.
