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MathNet 2026 — Part 07 Question 186

Math Olympiad Vault · MathNet 2026 — Part 07

Question 186

Find all possible values of $\frac{2 \cdot 3^{-x}-1}{3^{-x}-2}$, as $x$ runs through all real numbers.
  1. $(-\infty, 1 / 2) \cup (2,+\infty)$
  2. $(1 / 2,2)$
  3. $[2,+\infty]$
  4. $(0,+\infty)$