Given the functions f(x)=|x|, g(x)=6x-8, h(x)=4-x find u=fo(gof)/h .

Expert Answers info

justaguide eNotes educator | Certified Educator

calendarEducator since 2010

write12,544 answers

starTop subjects are Math, Science, and Business

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)|

check Approved by eNotes Editorial

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)|

check Approved by eNotes Editorial

Unlock This Answer Now