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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Functions

NDA 2025 · Mathematics · Functions

Consider the following for the two (02) items that follow: Let the...

Consider the following for the two (02) items that follow:
Let the curve f(x)=∣x−3∣f(x) = |x - 3|.

What is the domain of the function f(x)f(x)?

Options

  1. A(0,∞)(0, \infty)
  2. B(3,∞)(3, \infty)
  3. C(−∞,∞)(-\infty, \infty)
  4. D(−∞,∞)∖{3}(-\infty, \infty) \setminus \{3\}

Correct answer

C. (−∞,∞)(-\infty, \infty)

Step-by-step solution

The given function is f(x)=∣x−3∣f(x) = |x - 3|.

The expression x−3x - 3 is a linear polynomial, which is defined for all real values of xx.

The absolute value function is also defined for all real numbers.

Thus, f(x)f(x) is defined for all x∈Rx \in \mathbb{R}.

The domain of f(x)f(x) is (−∞,∞)(-\infty, \infty).

Answer: (−∞,∞)(-\infty, \infty)
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