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If f(x)={x, when x is rational and 0, wh...

If `f(x)={x,` when `x` is rational and `0,` when `x` is irrational `g(x)={0,` when `x` is rational and `x,` when `x` is irrational then `(f-g)` is

A

one-one and into

B

neither one-one nor onto

C

many-one and onto

D

one-one and onto

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)={{:(x-0,=x","x" is rational "),(0-x=-x",",x" is irrational"):}`
Clearly, f-g is one-one and onto.
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