The function f(x) = x2 = x + x …… x times, is defined A. at all real values of x B. only at positive integer values of x C. only at negative integer value of x D. only at rational values of x

The correct answer is A.

The function $f(x) = x^2 = x + x …… x$ times, is defined at all real values of $x$. This is because the expression $x + x …… x$ times is simply $x^2$, which is defined for all real values of $x$.

Option B is incorrect because the function is defined for negative integer values of $x$ as well. For example, $f(-1) = (-1)^2 = 1$.

Option C is incorrect because the function is defined for rational values of $x$ as well. For example, $f(1/2) = (1/2)^2 = 1/4$.

Option D is incorrect because the function is defined for irrational values of $x$ as well. For example, $f(\pi) = (\pi)^2 = \pi^2$.