Q118 / 160 · WBJEE 2011 · Mathematics
The even function of the following is
- A\(f(x)=\frac{a^x+a^{-x}}{a^x-a^{-x}}\)
- B\(f(x)=\frac{a^x+1}{a^x-1}\)
- Correct answerC\(f(x)=x \cdot \frac{a^x-1}{a^x+1}\)
- D\(\mathrm{f}(\mathrm{x})=\log _2\left(\mathrm{x}+\sqrt{\mathrm{x}^2+1}\right)\)
Solution
Hints: \(f(-x)=(-x) \frac{a^{-x}-1}{a^{-x}+1}\)
\(\begin{aligned}
& =(-n) \frac{1-a^x}{1+a^x} \\
& =n \frac{\left(a^x-1\right)}{\left(a^x+1\right)}=f(x)
\end{aligned}\)
Hence, the correct answer is option: 'C'.