Homework Help

For the following functions f&g,  f(x)=9x^2-4x+8  & g(x)=2√x determine...

user profile pic

erika-valladares | Student, Undergraduate | eNotes Newbie

Posted October 3, 2011 at 9:09 AM via web

dislike 2 like

For the following functions f&g,  f(x)=9x^2-4x+8  & g(x)=2√x determine  

(a) f(g(x))        (b) f(f(x))

2 Answers | Add Yours

user profile pic

locater | Student, Undergraduate | (Level 1) eNoter

Posted October 16, 2011 at 11:36 AM (Answer #1)

dislike 2 like

Composite Function

A) f(g(x))=9(2√x)^2-4(2√x)+8

 

B) f(f(x))=9(9x^2-4x+8)^2-4(9x^2-4x+8)+8

user profile pic

t-rashmi | College Teacher | (Level 3) Assistant Educator

Posted September 7, 2013 at 8:34 AM (Answer #2)

dislike 2 like

Given:

f(x) = 9x2 - 4x + 8 and 

g(x) = 2√x

To solve :

A] f(g(x))

B] f(f(x))

Solution :

A] f(g(x))

    = f(2√x)

    = 9(2√x)2 - 4(2√x) + 8

    = 36x - 8√x + 8

B] f(f(x))

    = f(9x2 - 4x + 8)

    = 9(9x2 - 4x + 8)2 - 4(9x2 - 4x + 8) + 8

    = 729x^4 - 648x^3 + 1440x^2 - 576x + 576 - 36x2 + 16x -32 + 8

    = 729x^4 - 648x^3 + 1404x^2 - 560x + 552


Hope this helps!

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes