Domain restriction:
When describing domain, we often say all real numbers. But that doesn't mean that all real numbers must be the values of the domain x. There are restrictions on domain.
In domain restrictions, it depends solely on the type of function.
For example, there are 2 reasons for domain restriction:
1) The square or root of a negative number cannot be used because the result is not a real number.
2) You should not divide by zero
Example:
If x=0, that means we will be dividing by zero, and since we cannot divide by zero, x cannot be zero.
Composite of function:
The domain of a composite function f o g, here, it will be dependent on thendomain of g and f
Example:
Given: f(g(x))
The domain of the composite function will be x values in the domain of g where g(x) is the domain of f.
Here, we are to find the domain of g and the domain of f.
When determining the domain of a composite function, restrictions on the starting function should be considered.
If any given input does not get through the starting function, it cannot get through the whole composition.