JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

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Analyzing +4 | -1

f:R \to R

is defined by

f\left( x \right) = x - \left[ x \right] - \frac{1}{2}\;for\;x \in R

, where

\left[ x \right]

is the greatest integer not exceeding

x

, then

\left\{ {x \in R:f\left( x \right) = \frac{1}{2}} \right\}

is equal to

View answer and explanation

Correct option: C

\phi

, the empty set

Option C (

\phi

, the empty set) is correct because the equation

f(x) = \frac{1}{2}

leads to a contradiction, meaning there are no real solutions.

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