COMEDK · Maths · 1. Basic of Mathematics
The function \(f(x)=\log \left(x+\sqrt{x^{2}+1}\right)\) is
- A an even function.
- B an odd function.
- C a periodic function.
- D neither an even nor an odd function.
Answer & Solution
Correct Answer
(B) an odd function.
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\log \left(x+\sqrt{x^{2}+1}\right)\) \(\therefore \quad f(x)+f(-x)=\log \left(x+\sqrt{x^{2}+1}\right)\) \(\quad+\log \left(-x+\sqrt{x^{2}+1}\right)=\log (1)=0\) \(\Rightarrow \quad f(-x)=-f(x)\) Hence, \(f(x)\) is an odd function.
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