Function Compositions

Adding/subtracting functions

100

f(x) = x+1

g(x) = x+2

Find (f+g)(x)

(f+g)(x) = 2x+3

200

f(x) = x³+4

g(x) = x - 5

Find (f-g)(x)

(f-g)(x) = x³-x+9

300

f(x) = sqrt(x²+1)

g(x) = x^4-5

Find (f+g)(x)

(f+g)(x) = sqrt(x²+1) + x⁴ - 5

400

f(x) = 1/x

g(x) = 1/x

Find (f-g)(x)

(f-g)(x) = 0

500

f(x) = 8x+3

g(x) = (x+2)²

Find (f-g)(x)

(f-g)(x) = -x²+4x-1

Multiplying/dividing functions

100

f(x) = x²

g(x) = x³

Find (f*g)(x)

(f*g)(x) = x⁵

200

f(x) = x⁵

g(x) = x³

Find (f/g)(x)

(f/g)(x) = x²

300

f(x) = x²-4

g(x) = x²+2x-8

Find (f/g)(x)

(f/g)(x) = (x+2)/(x+4)

400

f(x) = x⁴+8

g(x) = x²+3

Find (f*g)(x)

(f*g)(x) = x⁶+3x⁴+8x²+24

500

f(x) = x²-6x+9

g(x) = x²+5x-24

Find (f/g)(x)

(f/g)(x) = (x-3)/(x+8)

Plugging into combined functions

100

If (f/g)(x) = (x-3)/(x+8), find (f/g)(4).

(f/g)(4)=1/12

200

If (f+g)(x) = 5x⁴+3x²+4x+19, find (f+g)(2).

(f+g)(2) = 119

300

f(x) = x²-3

g(x) = x²+9

Find (f*g)(5).

(f*g)(5)= 748

400

f(x) = x⁴

g(x) = x³

Find (f/g)(4,153)

(f/g)(4,153) = 4153

500

f(x) = x+4

g(x) = 4x+7

Find f(g(3))

f(g(3)) = 23

Composition of functions

100

f(x) = x+1

g(x) = x+4

Find f(g(x))

f(g(x)) = x+5

200

f(x) = x²-7

g(x) = x²+2

Find g(f(x))

g(f(x)) = x⁴-14x²+51

300

f(x) = sqrt(x+4)

g(x) = x²+12

Find f(g(x))

f(g(x)) = sqrt(x²+16)

400

f(x) = x³+2

g(x) = 2/x

Find g(f(x))

g(f(x)) = 2/(x³+2)

500

f(x) = 1/4x²

g(x) = x²-7

Find f(g(4))

f(g(4)) = 1/324

Your SPTs

100

What are the two types of birds Jandy has?

Lovebirds and parakeets

200

What is Lyndsey's favorite band?

Bring Me the Horizon

300

How many siblings does Megan have?

0

400

How many years has Jandy been in America?

7 years as of yesterday!

500

What celebrity did Lyndsey meet? Hint: W.S.

William Shatner