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UPSC NDA I 2025 Mathematics Paper

Question Numbers: 85-86

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

Let the curve f(x) = | x - 3 |

Question : 85 of 120

Marks: +1, -0

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

Solution:

Concept:

The absolute value function

f(x)=|x-3|

is defined for every real number, because absolute value operates on any real input without restrictions.

Explanation:

The expression

|x-3|

does not involve division by zero, square roots of negatives, or logarithms. It simply returns the distance of

x

from 3 on the number line. Therefore, it accepts any real value of

x

. There are no excluded points or intervals.

Answer:

(-\infty, \infty)

– Option C

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