+900 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.
+1950
We basically just have to go thorugh every function and find when f(x) = x.
First, we have f(x) = 2x + 8.
We basically have 2x+8=x. Solving for this, we get x=−8. Unfortunately, that is not in the range 1≤x≤2, so that wouldn't work.
Second, we have f(x) = 13 - 5x.
We have 13−5x=x. Solving this, we get x=13/6. This is in the range 2<x≤3, so 13/6 is a valid solution
Third, we have f(x) = 20 - 14x.
We have 20−14x=x. Solving this, we get x=4/3. This is not in the range of 3<x≤4, so it is not a valid solution.
Lastly, we have f(x) = 40 + 5x.
We have 40+5x=x. Solving this, we get x=−10. This is not in the range 4<x≤5, so it is not a valid solution.
So finally, we have x=13/6.
Thanks! :)
