Zeros in a Solution Set

★ 8/10functions calculus Substitution Monotonicity

Problem

Let $f(x)$ be an odd differentiable function on $\mathbb{R}$ with $f(x) < f'(x)$ for $x > 0$ and $f(1) = e$ . Let $M$ be the solution set of

0 < f\left(\ln\left(x + \sqrt{1 + x^2}\right)\right) \leqslant x + \sqrt{1 + x^2}.

Find the number of zeros of $g(x) = \sin 6x$ on $M$ .

Answer

Solution

Difficulty	8/10
Topics	functions, calculus, Substitution, Monotonicity

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