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Question

Classify the following function f(x) defined in RR as injective, surjective, both or none

f(x)=x3+6x2+11x+6

A
Surjective but not injective
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B
Injective but not surjective
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C
Neither injective nor surjective
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D
Both injective and surjective
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Solution

The correct option is A Surjective but not injective
f(x)=x3+6x2+11x+6=0.
One one roots as x=1
Hence
f(x)=(x+1)(x2+5x+6)
=(x+1)(x+3)(x+2)
Hence
f(x)=0 has three roots 1,2,3
Hence y meets the x axis at three points.
Hence
The above function is surjective but it is not injective.

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