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Question

Assertion (A): Let f:RR be a function such that f(X)=X3+X2+3X+sinX, then f is one to one .
Reason (R): f(x) is neither increasing nor decreasing function.

A
Both (A) and (R) are true and (R) is the correct explanation of (A).
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B
Both (A) and (R) are true and (R) is not the correct explanation of (A).
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C
(A) is true but (R) is false.
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D
(A) is false but (R) is true.
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Solution

The correct option is B (A) is true but (R) is false.
f(X)=X3+X2+3X+sinX
f(X)=3X2+2X+3+cosX
f(X)=3(X2+23X+1)+cosX
f(X)=3(X+13)2+83+cosX
Clearly, f(X)>0
Hence the function is monotonically increasing function and is one to one.
The assertion (A) is true but the reason (R) is false.

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