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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