Question

Let f(x )= π −x/x −3.

What is the greatest integer for which f(x ) is defined?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Answer 1

The greatest integer for which the function f(x) = π − x/x − 3 is defined is 2, as the function is not defined at x = 3 due to division by zero. Therefore, the answer is (C) 2.

Step-by-step explanation:

To determine the greatest integer for which the function f(x) = π − x/x − 3 is defined, we need to consider the domain of f(x). This function is defined for all real numbers except where the denominator is zero. The denominator is zero when x = 3. Therefore, the function is not defined at x = 3, but it is defined for integers less than 3.

Looking at the options provided:

• x = 0: The function is defined.
• x = 1: The function is defined.
• x = 2: The function is defined.
• x = 3: The function is not defined.
• x = 4: The function is defined.

However, since the denominator becomes zero at x = 3, the greatest integer for which the function is defined is just below this value, which is 2. So the correct answer is (C) 2.