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Comprehension

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

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

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NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. (0, ∞)
  2. (3,∞)
  3. (-∞, ∞)
  4. (-∞.∞)\3

Answer (Detailed Solution Below)

Option 3 : (-∞, ∞)
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Detailed Solution

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Calculation:

Given,

The function is , which is an absolute value function.

The domain of an absolute value function is all real numbers, because the absolute value function is defined for all values of x. The function handles both positive and negative inputs for x .

Since there are no restrictions or undefined points for the absolute value function, the domain is all real numbers.

∴ The domain of the function is

Hence, the correct answer is Option 3.

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