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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)

 Jun 8, 2019
 #1
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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)

 

cool cool cool

 Jun 8, 2019

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