Question

If $0<x_1<x_2$ which of following is true for $y={\sec }^{-1}x$.

• A. ${\sec }^{-1}{x}_1+{\sec }^{-1}{x}_2>{\sec }^{-1}\left(\frac{x_1+x_2}{2}\right)$
• B. ${\sec }^{-1}{x}_1+{\sec }^{-1}{x}_2<2{\sec }^{-1}\left(\frac{x_1+x_2}{2}\right)$
• C. ${\sec }^{-1}{x}_1>{\sec }^{-1}{x}_2$
• D. ${\sec }^{-1}{x}_1={\sec }^{-1}{x}_2$

Answer 1

The correct option is B ${\sec }^{-1}{x}_1+{\sec }^{-1}{x}_2<2{\sec }^{-1}\left(\frac{x_1+x_2}{2}\right)$