    Question

# Which of following statements is/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 to one.

A
I and II only
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B
II and III only
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C
III and I only
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D
I , II and III
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Solution

## The correct option is B I , II and IIIExplanation through examples:I. Let's assume f(x)=x and g(x)=−x. Both f(x) and g(x) are one-one, but f(x)+g(x)=0 is not one-one.∴ Statement I does not hold true.II. Let's assume f(x)=x and g(x)=x3. Both f(x) and g(x) are one-one, but f(x)⋅g(x)=x4 is not one-one.∴ Statement II does not hold true.III. Let's assume f(x)=sinx. Here, f(x) is an odd function, but it is not one-one.∴ Statement III does not hold true.∴ All three statements are incorrect.  Suggest Corrections  0      Similar questions  Related Videos   Animal Tissues
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