A Value Nobody Takes

Problem

Let $a\in\mathbb R$ . Suppose there exists a function $f(x)$ with domain $\mathbb R$ such that

1. for every $x_0\in\mathbb R$ , the value $f(x_0)$ equals either $x_0$ or $x_0^2$ ; and 2. the equation $f(x)=a$ has no real solution.

Find the range of $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Logic

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