Final answer:
The function f(x) = x^2 is continuous for all real numbers.
Step-by-step explanation:
To find the points where the function f(x) is continuous, we need to determine when the function is continuous at every point in its domain.
In this case, the function is defined as f(x) = x^2 if x is rational, and f(x) = x^2 if x is irrational.
Since the function is a polynomial, it is continuous for all real numbers. However, we need to check if f(x) is continuous at the points where x is rational and irrational.
When x is rational, f(x) = x^2 is continuous because it is a polynomial function and polynomials are continuous everywhere.
When x is irrational, f(x) = x^2 is also continuous because irrational numbers do not affect the continuity of a function. Therefore, the function f(x) = x^2 is continuous for all real numbers.