WBJEE · Maths · Functions
The even function of the following is
- A \(f(x)=\frac{a^x+a^{-x}}{a^x-a^{-x}}\)
- B \(f(x)=\frac{a^x+1}{a^x-1}\)
- C \(f(x)=x \cdot \frac{a^x-1}{a^x+1}\)
- D \(\mathrm{f}(\mathrm{x})=\log _2\left(\mathrm{x}+\sqrt{\mathrm{x}^2+1}\right)\)
Answer & Solution
Correct Answer
(C) \(f(x)=x \cdot \frac{a^x-1}{a^x+1}\)
Step-by-step Solution
Detailed explanation
Hints: \(f(-x)=(-x) \frac{a^{-x}-1}{a^{-x}+1}\) \(\begin{aligned} & =(-n) \frac{1-a^x}{1+a^x} \\ & =n \frac{\left(a^x-1\right)}{\left(a^x+1\right)}=f(x) \end{aligned}\)
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