One more question for Dr. Broverman C exam study guide

[YKT]

Dr. Broverman,

In your C exam study manual V.2 P.SI-9 question #1, the solution shows F(x)=2x-1/2 if 1/2<= x <= 3/4 then the answer is 2x-1/2=.716 and x=.608.

However, I couldn't find F(x)=2x-1/2, what I could find is F(x)=2x-1 and anwser is 0.858.

Can you show me how to find F(x)=2x-1/2??


Thanks for your help.

[Sam Broverman]

YKT,

F(x) = integral from 0 to x f(t) dt .

We are given that f(t) = 1 for 0<t<.5 and f(t) = 2 for .5<t<.75 .

If .5 <x <.75 , then

F(x) = integral from 0 to .5 f(t) dt + integral from .5 to x f(t) dt
= integral from 0 to .5 1 dt + integral from .5 to x 2 dt
= (1)(.5) + (2)(x-.5) = 2x - .5 .

SB