These are the graphs of the functions f, g and h.
a. For which values of x does g(x) > h(x) count?
b. For which values of x does f(x) > g(x) count?
c. We have the function notations f(x) = -0,5x^2 + 2x and h(x) = 2-4 for the graphs of f and h. Solve f(x) < h(x)
+128474 a. For which values of x does g(x) > h(x) count?
g(x) > h(x) on (-inf, 1) and on ( 4, inf)
b. For which values of x does f(x) > g(x) count?
f(x) > g(x) on ( 0, 4)
h. Solve f(x) < h(x)
I think h(x) is 2x - 4
So....we want to solve this
-(1/2)x^2 + 2x < 2x - 4 subtract 2x from both sides
-(1/2)x^2 < - 4
0 < (1/2)x^2 - 4
(1/2)x^2 - 4 > 0 multiply through by 2
x^2 - 8 > 0
x^2 > 8
This will be true when (-inf, - sqrt (8) ) and ( sqrt (8) , inf)
