Function Composition

Operations

100

f(x)= 20x+ 11

g(x)= x²

find (f+g)(2)

55

200

f(x)=3x-20

g(x)=2x

find 

(f/g)(4)

-1

300

f(x)= x²+8

g(x)= 

sqrtx

find (f-g)(9)

86

400

f(x)= 4x+8

g(x)= 12x+10

Find (f-g)(x)

-8x-2

500

f(x)= 

1/x 

g(x)= 5x²

find (f*g)(x)

5x

Composition w/ x-value

100

f(x)= 5x

g(x)=20x

find g(f(2))

200

200

f(x)=6x

g(x)=3x

find f(g(-6))

-108

300

f(x)= x²+9x

g(x)=(x+6)

find (f o g)(-2)

52

400

f(x)= 

1/(2x+9)

g(x)=30x

find 

(f o g)(1/3)

1/29

500

 f(x) = 3x² + 6 

 g(x) = 

sqrtx

f(g(10))

36

Composition w/o x-value

100

f(x) = 3x 

g(x) = -4x

find f(g(x))

-12x

200

g(x) = –6x + 5 

 h(x) = –9x – 11

 find g(h(x))

54x+71

300

f(x)= –2x + 9 

 g(x) = 

sqrt(x+4)

 find (g o f)(x)

sqrt(-2x+13)

400

f(x) = 

4/sqrt(x+9)

 g(x) = x²-9

 find  (f o g)(x)

4/x

500

 f(x) = 

1/x

 g(x) =

1/x

 

find (g o g)(x)=

x

Finding Inverses

100

What is the inverse of y=x+4

y=x-4

200

f(x)=2x^2-4

find f^-1(x)

Not Invertible or only x>0

y=sqrt(x+4)/2

300

What is the inverse of 

f(x)=4/x+6

f^-1(x)=4/(x-6)

400

Identify the inverse of the following.

y=sqrt(x+4)-5

y=(x+5)^2-4

500

Identify the inverse for the function.

f(x)=2(x+5)^2-6

f^-1(x)=sqrt((x+6)/2)-5

Verifying inverses by composition

300

Verify algebraically that these two are inverses.f(x)=7x+3  and g(x)= 

(x-3)/7

f(x)=7x+3 and 

400

f(x)= 3x+1

g(x)= (x-1)/3

Does composition confirm they are inverses?

Yes!

500

Verify algebraically that these are inverses

f(x)=3/(x+5) and g(x)=(3x-5)/5

They are not

Random Trivia

100

What are human fingernails made of?

keratin

200

Who was the first person to walk on the moon?

Neil Armstrong

300

What are the two outermost colors on the upper and lower ends of a rainbow?

Red and Violet

400

What is the capital of Iceland?

Reykjavík

500

What is the national animal of Scotland?

Unicorn