Understanding an existence problem in terms of functions.

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Working on the book: Daniel J. Velleman. "HOW TO PROVE IT: A Structured Approach, Second Edition" (p. 150)

Example 3.6.3. Prove that for every real number $x$, if $x \neq 2$ then there is a unique real number $y$ such that $2y/(y + 1) = x$.

My questions:

  • Is it possible to rephrase it in terms of functions ?
  • Am I asked to show that the function $f(x)=2x/(x + 1)$ (domain: $\mathbb{R}-\{2\}$) has range = $\mathbb{R}$ ?