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Which of the following statements are incorrect?
$I. If f (x) and g (x) are one-one then f (x) + g (x) is also one-one$
$II. If f (x) and g (x) are one-one then f (x) \cdot g (x) is also one-one$
$III. If f (x) is odd then it is necessarily one-one.$

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II and III only

I and II only

III and I only

I, II and III

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detailed solution

Correct option is D

I. f(x)=x and g(x)=−x or f(x)=x and g(x)=−x3 II. f(x)=x and g(x)=x3 III. f(x)=sin⁡x which is odd but not one-one or f(x)=x2sin⁡x which is odd but many-one

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Which of the following statements are incorrect? I. If f(x) and g(x) are one-one then f(x)+g(x) is also one-one II. If f(x) and g(x) are one-one then f(x)⋅g(x) is also one-one III. If f(x) is odd then it is necessarily one-one.

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Which of the following statements are incorrect?
$I. If f (x) and g (x) are one-one then f (x) + g (x) is also one-one$
$II. If f (x) and g (x) are one-one then f (x) \cdot g (x) is also one-one$
$III. If f (x) is odd then it is necessarily one-one.$