MA 432 | Review (Chs 5.1-5.2)

Adding Functions

100

Find f(x) + g(x)

if 

f(x)=x-3

and

g(x)=x^3+2-2x

[f+g](x)=f(x)+g(x)=x^3-x-1

200

Find f(x) + g(x)

if 

f(x)=3x-3

and

g(x)=-x^2-3

[f+g](x)=f(x)+g(x)=-x^2+3x-6

Subtracting Functions

100

Find f(x) - g(x)

if 

f(x)=-4x

and

g(x)=x^2+4

Remember to distribute the negative!

[f-g](x)=f(x)-g(x)=-x^2-4x-4

200

Find f(x) - g(x)

if 

f(x)=4x+4

and

f(x)=x^2+5x

Remember to distribute the negative.

[f-g](x)=f(x)-g(x)=-x^2-x+4

Multiplying Functions

100

Find f(x) • g(x)

if

f(x)=3x-3

and

g(x)=2x^3-x^2

FOIL!

[f•g](x)=f(x)•g(x)=6x^4-9x^3+3x^2

200

Find f(x) • g(x)

if

f(x)=x^3+4x^2

and

g(x)=x+5

FOIL!

[f•g](x)=f(x)•g(x)=x^4+9x^3+20x^2

Dividing Functions

100

Find f(x)/g(x)

if

f(x)=-2x+3

and

g(x)=2x+1

Just write it as a fraction.

[f/g](x)=f(x)/g(x)=(-2x+3)/(2x+1)

200

Find f(x)/g(x)

if

f(x)=4x

and

g(x)=-3x+4

Just write the fraction.

[f/g](x)=f(x)/g(x)=(4x)/(-3x+4)

Composing Functions

100

Find f(g(x))

*meaning put g(x) in for x in the f(x) function

if

f(x)=x+3

and

g(x)=x+3

f(g(x))=f(x+3)=(x+3)+3=x+6

200

Find f(g(x))

*meaning put g(x) in for x in the f(x) function

if

f(x)=2x+3

and

g(x)=x^2 +1

f(g(x))=f(x^2+1)=2(x^2+1)+3=2x^2+2+3=2x^2+5