If \( f: R \rightarrow R \) given by \[ f(x)=x^{3}+(a+2) x^{2}+3 a x+5 \] is one-one, then a bel...

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If \( f: R \rightarrow R \) given by
\[
f(x)=x^{3}+(a+2) x^{2}+3 a x+5
\]
is one-one, then a belongs to the interval
(A) \( (-\infty, 1) \)
(B) \( (1, \infty) \)
(C) \( (1,4) \)
(D) \( (4, \infty) \)
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