Homework Help

Let g(x)=2x and h(x)= x^2+4. FInd each value or expression (g*g)(a) & (h*h)(a)

user profile pic

connorcolin3 | Valedictorian

Posted January 7, 2013 at 10:00 PM via web

dislike 0 like

Let g(x)=2x and h(x)= x^2+4. FInd each value or expression

(g*g)(a) & (h*h)(a)

1 Answer | Add Yours

user profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted January 8, 2013 at 1:35 AM (Answer #1)

dislike 1 like

Since `g(x)=2x` , then the composition is:

`g circ g(a)`

`=g(g(a))`

`=g(2a)`  now sub in the function

`=2(2a)`  simplify

`=4a`

Also, since `h(x)=x^2+4` , the composition is:

`h circ h(a)`

`=h(h(a))`

`=h(a^2+4)`  sub in the function

`=(a^2+4)^2+4`  simplify the brackets

`=a^4+8a^2+16+4`  simplify the expression

`=a^4+8a^2+20`

The compositions are `g circ g(a)=4a` and `h circ h(a)=a^4+8a^2+20` .` `

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes