f( x )= array l x , if x is rational 0, if x is irrational array . and g( x )= array l 0…
Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions
\(f(\mathrm{x})=\left\{\begin{array}{l}
\mathrm{x}, \text { if } \mathrm{x} \text { is rational } \\
0, \text { if } \mathrm{x} \text { is irrational }
\end{array}\right.\) and
\(g(\mathrm{x})=\left\{\begin{array}{l} 0, \text { if } \mathrm{x} \text { is rational } \\ \mathrm{x}, \text { if } \mathrm{x} \text { is irrational } \end{array}\right.\). Then, f – g is
\(g(\mathrm{x})=\left\{\begin{array}{l} 0, \text { if } \mathrm{x} \text { is rational } \\ \mathrm{x}, \text { if } \mathrm{x} \text { is irrational } \end{array}\right.\). Then, f – g is
- one-one and into
- neither one-one nor onto
- many one and onto
- one-one and onto
Answer
(D) one-one and onto
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