at all real values of x
only at positive integer values of x
only at negative integer value of x
only at rational values of x
Answer is Right!
Answer is Wrong!
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, $f(\pi) = (\pi)^2 = \pi^2$.