Question

can some help me understand domain and range

Answer 1

The domain is all the possible inputs of a function.
The range is all the possible outputs.

A function's domain can be arbitrarily decided; however, the natural domain of a function will by all inputs that have a defined output.

For example, consider the function: \[
f(x) = \sqrt{x-4}
\]If we do not consider complex or imaginary numbers, then this function will not be defined when \(x=4\) is below \(0\), because we couldn't take the square root of negative numbers.

Answer 2

Should have put \(x-4\)

Answer 3

Consider the function \[
f(x) = x^2
\]This function can never output negative numbers, if we ignore complex numbers. Thus it's range would be positive real numbers.