Given the functions f(x)=|x|, g(x)=6x-8, h(x)=4-x find u=fo(gof)/h .
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justaguide
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We have the functions: f(x)=|x|, g(x)=6x-8 and h(x) = 4-x. We have to find u= fo(gof)/h.
u = fo(gof)/h
=> u = fo[(g(f(x))/ h(x)]
=> u = fo[(6|x| - 8) / (4 - x)]
=> u = |(6|x| - 8)|/ |(4 - x)|
The required value of u = |(6|x| - 8)|/ |(4 - x)|
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giorgiana1976 | Student
We'll start by composing g and f:
gof = g(f(x)) = 6*f(x) - 8
gof = 6|x| - 8
We'll calculate (gof)/h:
(gof)/h = (6|x| - 8)/(4-x)
Now, we'll compose fo[(gof)/h]
fo[(gof)/h] = f[(gof)/h] = |fo[(gof)/h]|
fo[(gof)/h] = |(6|x| - 8)/(4-x)|
u(x) = |(6|x| - 8)|/|(4-x)|
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