If f(x) = l x, , , when , , ,x , , ,is , , ,rational , , 0 , , , … - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}x,\,\,{\rm{when\,\,}}\,x\,\,{\rm{\,is\,}}\,{\rm{\,rational\,\,}}\\0{\rm{,}}\,\,{\rm{when\,\,}}x{\rm{ \,\,is\,\,\, irrational\,}}\end{array} \right.$;$g(x) = \left\{ \begin{array}{l}0,\,\,\,\,{\rm{when\,\,}}\,x\,{\rm{\,\,is\,\,}}\,{\rm{\,\,rational\,}}\\x,\,\,\,\,{\rm{\,\,when\,\,}}\,x\,{\rm{\,\,is\,\, irrational\,}}\end{array} \right.$ then $(f - g)$ is

✓
One $-$ one onto
B
One $-$ one not onto
C
Not one $-$ one but onto
D
Not one $-$ one not onto

✓

Answer

Correct option: A.

One $-$ one onto

$(f - g)(x) = \left\{ \begin{array}{l}\,\,\,x,\,\,x \in Q\\ - x,\,\,\,x \notin Q\end{array} \right.$

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