One Symmetric Pair

★ 7/10functions Reflection Logarithms Casework

Problem

Let

f(x) = \begin{cases} \log_a x, & x > 0,\\ |x + 3|, & -4 \leqslant x < 0, \end{cases}

where $a > 0$ and $a \neq 1$ . If the graph of $f(x)$ contains exactly one pair of points symmetric about the $y$ -axis, find the range of possible values of $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Reflection, Logarithms, Casework

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