A) Both statements are True, Statement-2 explains Statement-1.
B) Both statements are True, Statement-2 does not explain Statement-1.
C) Statement-1 is True, Statement-2 is False.
D) Statement-1 is False, Statement-2 is true.
Correct Answer: B
Solution :
\[f(x)={{x}^{3}}+6x+9x+\sin x\] \[f'(x)=3{{x}^{2}}+6x+9+\cos x>5\,\forall \,x\] as \[3{{x}^{2}}+6x+9\ge 6\,\forall \,x\] \[\Rightarrow \,\,f(x)\] is strictly increasing function, whose range is R, hence exactly one real root. Also, \[f(x)\] is one-one. \[\therefore \,\,\,\,f(a)\ne \,f(b)\,\forall \,a,\,b\,\in \,R,\,a\ne b\]You need to login to perform this action.
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