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 (fg)(x)

5x

Composition w/ x-value

100

f(x)=6x

g(x)=3x

find f(g(-6))

-108

200

f(x)= x²+9x

g(x)=(x+6)

find (f o g)(-2)

52

300

f(x)=logx

g(x)=sinx+99

Find f(g(pi/2))

2

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) = sin²x

 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

Find the inverse of y=1+logx

y=e^x-1

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)=2x^2+20x-44

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

Composition of functions

100

f(x) = x²+x

g(x) = x²+x

f(g(x))=?

f(g(x))=x⁴+2x³+2x² +x

200

f(x)=x-3

g(x)=x²+1

For what x does f(g(x))=g(f(x))

x=2

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

Domains

100

f(x)=sinx

g(x)= log₃x

What is the domain of (f/g)(x)

D: (0,1)U(1, infinity)

200

g(x)= 

sqrtx

f(x) = x²

What is the domain of f(g(x))?

D: [0, infinity)

300

f(x) = e^x

g(x) = 

sqrtx

What is the domain of g(f(x))?

D: (-infinity, infinity)

400

f(x)= 

1/(x-2)

g(x)=

sqrt(x+1)

What is the domain of f(g(x))

D: [-1,3)U(3, infinity)

500

f(x)=log₆x

g(x)=x²-36

determine the domain of f(g(x))

(-infinity,-6)U(6,infinity)