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Question

Let f:RR be a function defined by f(x)=x3+x2+3x+sinx. Then f is

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

The correct option is A one-one and onto
f(x)=x3+x2+3x+sinx, xR
f(x)=3x2+2x+3+cosx
f(x)=g(x)+cosx
g(x)>0 [D=436=32<0]
Range of g(x) is [D4a,)
[+3212,)=[83,)

f(x)>0
Hence, function is strictly increasing.
limxf(x)=
and limxf(x)=
Function is one-one and onto as f(x) is continuous function.

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