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• Hi! I need help with these Algebra 2 questions about "Operations on Functions". If you could help me, I would honestly be so thankful!

# Algebra/Hi! I need help with these Algebra 2 questions about "Operations on Functions". If you could help me, I would honestly be so thankful!

Question
1.) f(x)= x^2-3x+2; g(x)= 2x+4. Find the following:

a.) (f+g)(x)
b.) (f-g)(x)
c.) (f * g)(x)
d.) (f/g)(x)

2.) f(x)= { (2,3), (4,4), (5,8) }; g(x)= { (2,4), (3,5), (4,2) } Find the following: (if they exist)

a.) (FoG)(x)
b.) GoF)(x)

3.) g(x)=x^2+2x01, h(x)=x-4. Find the following:

a.) (GoH)(x)
b.) (HoG)(x)

4.) f(x)= 3x-2, g(x)=x^2+1. Find the following:

a.) f [g(-3)]
b.) g[f(-3)]

Hello Julia,

1.
a.) (f+g)(x)=f(x)+g(x)=x^2-3x+2 + 2x+4 = x^2-x+6
b.) (f-g)(x)=f(x)-g(x)=x^2-3x+2 - (2x+4) = x^2-5x-2
c.) (f * g)(x)=f(x)*g(x)=(x^2-3x+2)*(2x+4)
d.) (f/g)(x)=f(x)/g(x)=(x^2-3x+2)/(2x+4)

2.
a.) (FoG)(x)=F(G(x)), using the input (i.e x-values) of G, thus
.    F(G(2))=F(4)=4 ==> (2,4)
.    F(G(3))=F(5)=8 ==> (3,8)
.    F(G(4))=F(2)=3 ==> (4,3)
.    Giving {(2,4), (3,8), (4,3)}
b.) (GoF)(x)=G(F(x))...similarly we get: {(2,5), (4,2)}, since when x=5, F(5)=8 but G(8) is undefined.

3.
a) (GoH)(x)=G(H(x))=G(x-4)=(x-4)^2+2(x-4)-1 (I gather that "0" should be "-"...yes???)
b) (HoG)(x)=H(G(x))=H(x^2+2x-1)=x^2+2x-1-4=x^2+2x-5

4.
a) f(g(-3))=f((-3)^2+1)=f(10)=3(10)-2=28
b) g(f(-3))=g(3(-3)-2)=g(-11)=(-11)^2+1=122

OK?  I hope this helps!  :-)

TTYL, Abe

Algebra

Volunteer

#### Abe Mantell

##### Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

##### Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook