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Question

Let f:NN be defined by f(x)=x2+x+1,xN. Then f is

A
one-one onto
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B
many-one onto
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C
one-one but not onto
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D
none of these
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Solution

The correct option is B one-one but not onto
f(x)=x2+x+1
For xN
f(x)3
That is, its range of values includes all the natural numbers greater than and equal to 3.
However f(x1)=f(x2)
x1=x2
Hence f(x) is a one-one function but not an onto function.

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