ARITHMETIC COMBINATIONS OF FUNCTIONS WORKSHEET

Finding Arithmetic Combinations of Functions

Find

a) (f + g)(x)

b) (f - g)(x)

c) (fg)(x) and

d) (f/g)(x).

e)  What is the domain of f/g?

Problem 1 :

f(x) = x + 3, g(x) = x - 3

Solution

Problem 2 :

f(x) = 2x - 5, g(x) = 1 - x

Solution

Problem 3 :

f(x) = 3x², g(x) = 6 - 5x

Solution

Problem 4 :

f(x) = 2x + 5, g(x) = x² - 9

Solution

Problem 5 :

f(x) = x² + 5, g(x) = √1 - x

Solution

Problem 6 :

f(x) = √x² - 4, g(x) = x² / x² + 1

Solution

Problem 7 :

f(x) = 1/x, g(x) = 1/x²

Solution

Problem 8 :

f(x) = x/x + 1, g(x) = 1/x³

Solution

Answer Key

Problem 1 :

a)  (f + g)(x) = 2x

b)  (f - g)(x) = 6

c)  (fg)(x) = x² - 9

d)  (f/g)(x) = (x + 3) / (x - 3)

e)  Domain : All real values except 3

Problem 2 :

a)  (f + g)(x) = x - 4

b)  (f - g)(x) = 3(x - 2)

c)  (fg)(x) = 2x² - 7x + 5

d)  (f/g)(x) = (2x - 5) / (1 - x)

e)  Domain: All real values except 1

Problem 3 :

a)  (f + g)(x) = 3x² - 5x + 6

b)  (f - g)(x) = 3x² + 5x - 6

c)  (fg)(x) = 18x² - 15x³

d)  (f/g)(x) = 3x² / 6 - 5x

e)  Domain: All real values except 6/5

Problem 4 :  

a)  (f + g)(x) = x² + 2x - 4

b)  (f - g)(x) = x² - 2x - 14

c)  (fg)(x) = 2x³ + 5x² - 18x - 45

d)  (f/g)(x) = (2x + 5) / (x² - 9)

e)  Domain: (-∞, -3),(-3, 3) U (3, ∞)

Problem 5 :

a) (f + g)(x) = x² + 5 + √1 - x

b) (f - g)(x) = x² + 5 - √1 - x

c)  (fg)(x) = (x² + 5) √1 - x

d) (f/g)(x) = (x² + 5)√1 - x / (1 - x)

e)  Domain: All real values except 1

Problem 6 :

a)  (f + g)(x) = √x² - 4 + x² / (x² + 1)

b)  (f - g)(x) = √x² - 4 - x² / (x² + 1)

c)  (fg)(x) = (√x² - 4) (x² / (x² + 1))

d)  (f/g)(x) = (√x² - 4) / (x² / (x² + 1))

e)  Domain : All real values

Problem 7 :

a)  (f + g)(x) = (x + 1) / x²

b)  (f - g)(x) = (x - 1) / x²

c)  (fg)(x) = 1/x³

d)  (f/g)(x) = x

e)  Domain : All real values

Problem 8 :

a)  (f + g)(x) = (x4 + x + 1) / (x4 + x³)

b)  (f - g)(x) = (x4 - x - 1) / (x4 + x³)

c)  (fg)(x) = 1/(x³ + x²)

d)  (f/g)(x) = x4 / (x + 1)

e)  Domain: All real values except -1

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