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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1
If f:R→Rf:R \to R is given by
f(x)={−1,  when    x    is    rational1,  when    x    is    irrational,f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} { - 1,\;when\;\;x\;\;is\;\;rational}\\ {1,\;when\;\;x\;\;is\;\;irrational} \end{array}} \right.,
Then (fof)(1−3)\left( {fof} \right)\left( {1 - \sqrt 3 } \right) is equal to
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Correct option: B
−1- 1
Option B (-1) is correct because the function f(x) returns -1 for rational numbers and 1 for irrational numbers. Since 1 - √3 is irrational, f(1 - √3) = 1, which is rational, so f(1) = -1.

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