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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!

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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)]

Answer
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

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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

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