Homework Help

Let f(x)=x^2 and g(x)=x-3. Evaluate each expression. 1. `(f _og)(-2)` and `(g_og)(7)`  

user profile pic

vipergrooms | Student, Undergraduate | (Level 1) eNoter

Posted May 15, 2013 at 1:59 AM via web

dislike 2 like

Let f(x)=x^2 and g(x)=x-3. Evaluate each expression.

1. `(f _og)(-2)` and `(g_og)(7)`

 

2 Answers | Add Yours

Top Answer

user profile pic

oldnick | (Level 1) Valedictorian

Posted May 15, 2013 at 3:45 AM (Answer #2)

dislike 3 like

`f[g(x)]=(x-3)^2`          `f[g(-2)]=(-2-3)^2=25`

 

`g[g(x)]=(x-3)-3=x-6`       `g[g(7)]=7-6=1`

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted May 15, 2013 at 2:16 AM (Answer #1)

dislike 1 like

This is about composition of function.

In `(f_0g)(x)` we have to replace x in f(x) terms of x in g(x).

`f(x) = x^2`

`g(x) = x-3`

 

`(f_0g)(x) = (x-3)^2`

`(g_0g)(x) = (x-3-3) = (x-6)`

 

Then we can write the answers as;

`(f_0g)(-2) = (-2-3)^2 = 25`

`(g_0g)(7) = (7-6) = 1`

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes