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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a
II and III only
b
I and II only
c
III and I only
d
I, II and III
answer is D.
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Detailed Solution
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)=sinx which is odd but not one-one or f(x)=x2sinx which is odd but many-one