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Question

# If f:R→R 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 functionf(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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