Mathematics · 2013
JEE Main · 25 April 2013, Shift 1 · Q84
Consider the function: f(x)=[x]+|1-x|,-1 ≤ x ≤ 3 where [x] is the greatest integer function. Statement I: f is not continuous at x=0,1,2 and 3.…
Consider the function :
$$f(x)=[x]+|1-x|,-1 \leq x \leq 3 \text { where }[x]
$$
is the greatest integer function.
Statement I : $\displaystyle f$ is not continuous at $\displaystyle x=0,1,2$ and 3.Statement II : $\displaystyle f(x)=\left(\begin{array}{cc}-x, & -1 \leq x<0 \\ 1-x, & 0 \leq x<1 \\ 1+x, & 1 \leq x<2 \\ 2+x, & 2 \leq x \leq 3\end{array}\right.$
Official answer
(1)
Statement I is true ; Statement II is false.
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JEE Main 2013 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.