Find all constants $A$, $B$ such that the function $f: \mathbb{R} \to \mathbb{R}$, $f(x) = \begin{cases} 2x + A, & x < 0 \ \frac{1}{2}x + B & x \ge 0 \end{cases}$ is a injective but not surjective.
Added by Guillermo N.
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A function is injective if and only if it has a unique output for every input. In other words, if f(x1) = f(x2), then x1 = x2. In our case, the function is 2x + A for x < 0 and 2x + B for x > 0. To ensure injectivity, we need to make sure that for any two Show more…
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