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Question

If f:RR is defined by f(x)=x+x2, then f is

A
an injective function
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B
an onto function
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C
a bijecive function
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D
neither a one one nor an onto function
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Solution

The correct option is D neither a one one nor an onto function
f(x)=x+x2
f(x)=x+|x|
When x is negative
f(1)=1+|1|=0f(2)=2+|2|=0f(3)=3+|3|=0
f(x) is a many-one function.

Also f(x)=x+|x|
We have seen that when x is negative, f(x) is always 0.
Now when x is positive,
f(x)=2x
Hence the range would be [0,)
f(x) is not an onto function since its range is not equal to its co-domain.
f(x) is neither one-one nor onto function.

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