Question

Let $f(x) = 1 + x\log\left(x + \sqrt{x^2+1}\right) - \sqrt{x^2+1}, \; x \geq 0$. Then:

• A. $f(x)$ is increasing on $(0,\infty)$
• B. $f(x)$ is increasing only on $(10,\infty)$
• C. $f(x)$ is increasing only on $(0,e)$
• D. $f(x)$ is decreasing on $(0,\infty)$
• E. $f(x)$ is decreasing only on $(100,\infty)$

Hint:

$\log(x+\sqrt{x^2+1})$ is always positive for $x>0$.

Answer 1

The Correct Option is A