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The function f(x) is defined for 1 \le x \le 5 as follows:
-2x + 4 & \text{if }1 \le x \le 2, \\
5 - x & \text{if }2 < x \le 3, \\
9 - 2x & \text{if }3 < x \le 4, \\
6 - x & \text{if }4 < x \le 5.

Find all real numbers x such that f(x) = 18.

 

If you find more than one answer, list them all, separated by commas.

 Feb 16, 2024
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There is no real number solution within the given domain of \(f(x)\).
First solve all 4 equations and check if the value of \(x\) lands in its own domain.
For ex:

\(-2x+4=18\\ x=-7 \notin1\le x\le 2\)

All the other equations lead to neagative answers and those are not in \(1 \le x \le 5\)
Therefore there are no real solutions to this piece-wise function

 Feb 16, 2024

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