SOLUTION: Determine the set of points where f (x) ≥ g (x), if f (x) = x2 – 4x and g (x) = x – 6. You may solve this either algebraically or graphically by graphing calculator.

Algebra ->  Permutations -> SOLUTION: Determine the set of points where f (x) ≥ g (x), if f (x) = x2 – 4x and g (x) = x – 6. You may solve this either algebraically or graphically by graphing calculator.      Log On


   

Question 869249: Determine the set of points where f (x) ≥ g (x), if f (x) = x2 – 4x and g (x) = x – 6. You may solve this either algebraically or graphically by graphing calculator.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the points where the functions cross each other.
f%28x%29=g%28x%29
x%5E2-4x=x-6
x%5E2-5x%2B6=0
%28x-2%29%28x-3%29=0
Two solutions:
x-2=0
x=2
and
x-3=0
x=3
So break up the number line into three regions and test the inequality.
x%3C2
x=0
0-4%3E0-6
-4%3E-6
True
2%3Cx%3C3
x=5%2F2
%285%2F2%29%5E2-4%285%2F2%29%3E5%2F2-6
25%2F4-20%2F2%3E5%2F2-12%2F2
25%2F4-40%2F4%3E-7%2F2
-15%2F4%3E-14%2F4
False
x%3E3
x=4
4%5E2-4%284%29%3E4-6
0%3E-2
True
So now put it all together.
(-infinity,2]U[3,infinity)