Final Answer:
The expression (f ° f)(x) represents the composition of the function f with itself. The domain of (f ° f)(x) is [-∞, ∞].
Step-by-step explanation:
The expression (f ° f)(x) represents the composition of the function f with itself. To find the domain of (f ° f)(x), we need to consider the domain of the function f. Since the composition of functions involves applying one function to the output of another, the domain of (f ° f)(x) will be determined by the domain of f.
Assuming f(x) is a function that doesn't have any restrictions or limitations on its domain, composing it with itself won't introduce any new constraints. Therefore, the domain of (f ° f)(x) will inherit the domain of f, which is the set of all real numbers, represented as [-∞, ∞] in interval notation.
In simpler terms, when you combine a function with itself (f ° f)(x), as long as the original function doesn't have any domain limitations (such as division by zero or square roots of negative numbers), the resulting domain remains unrestricted and encompasses all real numbers from negative infinity to positive infinity, [-∞, ∞].
This means that no matter what the function f(x) actually represents, when it's composed with itself, there are no new constraints or limitations introduced to its domain. Thus, the domain of (f ° f)(x) remains all real numbers from negative infinity to positive infinity, [-∞, ∞].