    Question

# Which of the following statements are incorrect?I If f(x) and g(x) are one to one then f(x) + g(x)II If f(x) and g(x) are one to one then f(x).g(x)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
I, II and III
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D
None of the above
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Solution

## The correct option is C I, II and IIILet f(x)=ax and g(x)=−bxBoth are injective, functionsf(x)+g(x)=ax−bx=x(a−b)Now for a special case where a=b we get f(x)+g(x)=0, hence a constant function.Therefore, A is incorrect.f(x)g(x)=−abx2Now we know that functions of type y=x2 or y=−x2 are many-one functions.That is f(x1)=f(x2)→x1=±x2 ...(hence many on one function).Consider f(x)=sin(x)f(−x)=−f(x), since sin(x) is odd function.However it is periodic with a period of 2πHence it is not one on one function.Hence all of the above are incorrect.  Suggest Corrections  0      Similar questions  Related Videos   MATHEMATICS
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