+1208 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.
+1946 For this problem, we have to go throug every function and find when f(x) = x.
First off, we have f(x)=2x+8.
We have to solve 2x+8=x, in which we get x=−8. However, -8 isn't in the range 1≤x≤2, so it isn't a valid solution.
Next, we have f(x)=13−5x
Solving for 13−5x=x, we get x=13/6. Indeed, 13/6 is in the range 2<x≤3, so it is a valid solution.
After, we have f(x)=20−14x
Solving for 20−14x=x, we get x=4/3, which is not a valid solution since it's not in the range 3<x≤4.
Lastly, we have f(x)=40+5x.
We have 40+5x=x, in which we get x=−10, which is not a valid solution.
So, we only have x = 13/6
Thanks! :)
