Question

Let $e$ be the eccentricity of a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, and $f\left(e\right)$ be the eccentricity of hyperbola $-\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, then ${\int }_1^3\underset{ntimes}{\underset{}{fff.....f\left(e\right)}}de$ is equal to

• A. $2$, if $n$ is even
• B. $4$, if $n$ is even
• C. $2\sqrt{2}$, if $n$ is odd
• D. $4\sqrt{2}$, if $n$ odd

Answer 1

Answer: (B), (C)

The correct options are
B $4$, if $n$ is even
C $2\sqrt{2}$, if $n$ is odd