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Question

# Which of the following statements is/are true?I: Every function must be either even or odd functionII: The function f(x)=log(x+√x2+1) is an odd function.

A
Only I is true
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B
Only II is true
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C
Both I and II are true
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D
Neither I nor II is true
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Solution

## The correct option is B Only II is trueI A function can be odd, even or neither odd nor even.II f(x)=log(x+√x2+1)f(−x)=log(√x2+1−x)f(−x)=log((√x2+1−x)×√x2+1+x√x2+1+x)=log(1√x2+1+x)=−log(x+√x2+1)f(−x)=−f(x)∴f(x) is an odd function

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