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Question

Let f:RR be a mapping such that f(x)=x21+x2.Then f is

A
many-one
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B
one-one
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C
into
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D
onto
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Solution

The correct options are
A many-one
C into
f(x)=x21+x2
It is clearly evident that, f(x)=f(x)
Therefore, f(x) is many-one.

Also, Since x20 and also 1+x2>0 for xR,

Therefore, f(x)0 for xR.
So, It does not take negative values.

Thus, It is into function.

Thus, the correct answers are A nd C.

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