Show:
Adding and
Subtracting Functions
Multiplying
Functions
Dividing
Functions
Composition of
Functions
Finding an
Inverse Function
100

How do you add and subtract functions?

** Hint: 3 words **

Combine like terms

100

After finding a common denominator, what operation do you do to the exponents?

Add the exponents

100

After finding a common denominator, what operation do you do to the exponents?

Subtract the exponents

100

f (x) = x + 3

h (x) = √(x – 7)


Find f(h(11))

f(h(11)) =5

100

How do you find the inverse of a function?

** Hint: 2 steps **

1. Switch x and y

2. Solve the equation for y

200

f (x) = –6√(x)

g (x) = 2√(x)


Find:

1. (f + g)(x)

2. The domain of (f + g)(x)

3. (f + g)(25)

1. (f + g)(x) = –4√(x)

2. Domain of (f + g)(x) = x ≥ 0

3. (f + g)(25) = –20

200

f (x) = 4x⅔

g (x) = 2x⅓


Find:

1. (fg)(x)

2. The domain of (fg)(x)

3. (fg)(–7)

1. (fg)(x) = 8x

2. Domain of (fg)(x) = All real numbers

3. (fg)(–7) = –56

200

f (x) = 4x5/4

g (x) = x½


Find:

1. (f/g)(x)

2. The domain of (f/g)(x)

3. (f/g)(81)

1. (f/g)(x) = 4x¾

2. Domain of (f/g)(x) = All real numbers except x = 0

3. (f/g)(81) = 108

200

f (x) = x + 3

g (x) = 4x2


Find g(f(–8))

g(f(–8)) = 100

200

Find the inverse of the function below:

f(x) = –½x + 10

f –1(x)= –2x + 20

300

f (x) = 2x2 + 11x

g (x) = –3x2 – 7x + 4


Find:

1. (f + g)(x)

2. The domain of (f + g)(x)

3. (f + g)(2)

1. (f + g)(x) = –x2 + 4x + 4

2. Domain of (f + g)(x) = All real numbers

3. (f + g)(2) = 8

300

f (x) = 3x2

g (x) = x¼


Find:

1. (fg)(x)

2. The domain of (fg)(x)

3. (fg)(16)

1. (fg)(x) = 3x9/4

2. Domain of (fg)(x) = x ≥ 0

3. (fg)(16) = 1,536

300

f (x) = 15x

g (x) = 3x¾


Find:

1. (f/g)(x)

2. The domain of (f/g)(x)

3. (f/g)(625)

1. (f/g)(x) = 5x¼

2. Domain of (f/g)(x) = All real numbers except x = 0

3. (f/g)(625) = 25

300

g (x) = 4x2

h (x) = √(x – 7)


Find h(g(2))

h(g(2)) = 3

300

Find the inverse of the function below:

f(x) = x3 – 12

f –1(x)= ∛(x + 12)

400

f (x) = 5∜(x)

g (x) = –19∜(x)


Find:

1. (f – g)(x)

2. The domain of (f – g)(x)

3. (f – g)(16)

1. (f – g)(x) = 24∜(x)

2. Domain of (f – g)(x) = x ≥ 0

3. (f – g)(16) = 48

400

f (x) = x3

g (x) = 2∛(x )


Find:

1. (fg)(x)

2. The domain of (fg)(x)

3. (fg)(8)

1. (fg)(x) = 2x10/3

2. Domain of (fg)(x) = All real numbers

3. (fg)(8) = 2,048

400

f (x) = 3√(x)7

g (x) = x3


Find:

1. (f/g)(x)

2. The domain of (f/g)(x)

3. (f/g)(144)

1. (f/g)(x) = 3x½

2. Domain of (f/g)(x) = All real numbers except x = 0

3. (f/g)(144) = 36

400

f (x) = 2x – 5

h (x) = 3x + 4


Find:

1. h(f(x))

2. The domain of h(f(x))

1. h(f(x)) = 6x – 11

2. Domain of h(f(x)) = All real numbers

400

Find the inverse of the function below:

f(x) = x2 + 8, x ≥ 0

f –1(x)= √(x – 8)

500

f (x) = 9x3 + 3x2 – 2x + 4

g (x) = 7x3 – 2x2 – 7x – 1


Find:

1. (f – g)(x)

2. The domain of (f – g)(x)

3. (f – g)(–2)

1. (f – g)(x) = 2x2 + 5x2 + 5x + 5

2. Domain of (f + g)(x) = All real numbers

3. (f + g)(2) = –1

500

f (x) = 7x3/2

g (x) = –3x⅓


Find:

1. (fg)(x)

2. The domain of (fg)(x)

3. (fg)(64)

1. (fg)(x) = –21x11/6

2. Domain of (fg)(x) = x ≥ 0

3. (fg)(64) = –43,008

500

f (x) = 5x3/2

g (x) = –10x⅓


Find:

1. (f/g)(x)

2. The domain of (f/g)(x)

3. (f/g)(64)

1. (f/g)(x) = –½ x7/6

2. Domain of (f/g)(x) = All real numbers except x = 0

3. (f/g)(64) = –64

500

g (x) = x–2

h (x) = 3x + 4


Find:

1. g(h(x))

2. The domain of g(h(x))

1. g(h(x)) = 1/(3x + 4)2

2. Domain of g(h(x)) = All real numbers except x = –4/3

500

Find the inverse of the function below:

f(x) = 3√(x + 5)

f –1(x) = 1/9 x2 – 5, x ≥ 0