+750 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.
+1953 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! :)
