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JEE MATHEMATICS MCQ: FUNCTIONS

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If the functions f(x)f(x) and g(x)g(x) are defined on R→RR \rightarrow R such that f(x)={0,x∈ rational x,x∈ irrational ;g(x)={0,x∈ irrational x,x∈ rational f(x)=\left\{\begin{array}{ll}0, & x \in \text { rational } \\ x, & x \in \text { irrational }\end{array} ; g(x)= \begin{cases}0, & x \in \text { irrational } \\ x, & x \in \text { rational }\end{cases}\right. then (f−g)(x)(f-g)(x) is
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Correct option: A
one-one and onto
Option A (one-one and onto) is correct because the function (f-g)(x) maps each real number to a unique real number, covering the entire real number set.

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