+635 The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4
f(x) = 40 + 5x if 4 < x \le 5
Find all real numbers x such that f(x) = x. If you find more than one answer, list them all, separated by commas.
+1926 We can go through every function to solve this problem.
First, we have \(x=2x+8\), because we want f(x) to equal x.
We solve this to find \(x=-8\). Unfortunately, this is not in the range given for x, so the solution is invalid.
Now, we have \(x=13-5x\).
Solving for this, we have \(x=13/6\). This is in the range given, so it is a valid solution.
Third, we have \(x=20-14x\).
We get \(x=4/3\). This is not in the range given, so the solution is invalid.
Lastly, we have \(x=40+5x\)
Solving for this, we get \(x=-10\). This is not in the range, so it is invalid.
So, the only solution is \(x=13/6\)
Thanks! :)
