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Consider the function f:Rto{0,1} such th...

Consider the function `f:Rto{0,1}` such that
`f(x)={{:(1","if ,x" is rational"),(0","if,"x is irratinal"):}`
Which one of the following is correct?

A

The function is one-one into

B

The function is many-one into

C

The function is one-one onto

D

The function is many-one onto

Text Solution

Verified by Experts

The correct Answer is:
C
Since, on taking a straight line parallel to x-axis, the group of given function intersect it at one point.
`:.` f(x) is one-one.
and as range of f(x)=Co-domain
`:.` f(x) is onto.
Hence, f(x) is one-one onto.
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