# Functions (2)

Algebra Level 4

Let $$f: (0, \infty) \to \mathbb R$$ be a function satisfying $$f(x) + e^{f(x)} = \dfrac2x - \ln x - 1$$. Find the range of $$x$$ satisfying the inequality $f(2x^2 + 1) - f(x^2 + 5) \geq f(1) .$,$$x>0$$

Notation: $$\mathbb R$$ denotes the set of real numbers.

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