Operations with Functions

Rules for Operating with Functions
Given functions f(x) and g(x)

Sum: (f + g)(x) = f(x) + g(x)
Difference: (f - g)(x) = f(x) - g(x)
Multiplication: (f・g)(x) = f(x)・g(x)
Division: (f ÷ g)(x) = f(x) ÷ g(x)

Given f(x) = 2x + 5 and g(x) = 4x + 2, find (f + g)(x).
Solution:
(f + g)(x) = f(x) + g(x)
Add the right-hand sides of the equations together:
2x + 5 + 4x + 2
Group like terms: 2x + 4x + 5 + 2
Combine like terms: 6x + 7 *Answer

Given f(x) = 5x + 3 and g(x) = 2x + 4, find (f + g)(x).
Solution:
(f + g)(x) = f(x) + g(x)
Add the right-hand sides of the equations together:
5x + 3 + 2x + 4
Group like terms: 5x + 2x + 3 + 4
Combine like terms: 7x + 7 *Answer

Given f(x) = 4x + 3 and g(x) = 6x + 2, find (f - g)(x).
Solution:
(f - g)(x) = f(x) - g(x)
Subtract the right-hand sides of g(x) from f(x):
4x + 3 - (6x + 2)
4x + 3 - 6x - 2
Group like terms: 4x - 6x + 3 - 2
Combine like terms: -2x + 1 *Answer

Given f(x) = 2x² + 3x + 6 and g(x) = 3x² + 7x + 10, find (f - g)(x).
Solution:
(f - g)(x) = f(x) - g(x)
Subtract the right-hand sides of g(x) from f(x):
2x² + 3x + 6 - (3x² + 7x + 10)
2x² + 3x + 6 - 3x² - 7x - 10
Group like terms:
2x² - 3x² + 3x - 7x + 6 - 10
Combine like terms: -x² - 4x - 4 *Answer

Given f(x) = 3x + 5 and g(x) = 2x + 4, find (f・g)(x).
Solution:
(f・g)(x) = f(x)・g(x)
Multiply the right-hand sides of the equations together.
(3x + 5)(2x + 4) Use FOIL
6x² + 12x + 10x + 20
6x² + 22x + 20 *Answer

Given f(x) = 4x - 6 and g(x) = 2x² + 4, find (f・g)(x).
Solution:
(f・g)(x) = f(x)・g(x)
Multiply the right-hand sides of the equations together.
(4x - 6)(2x² + 4) Use FOIL
8x³ + 16x - 12x² - 24
8x³ - 12x² + 16x - 24 *Answer

Given f(x) = 24x² and g(x) = 2x, find (f ÷ g)(x).
Solution:
(f ÷ g)(x) = f(x) ÷ g(x)
Divide the first equation by the second equation.
(24x²) ÷ (2x)
(24 ÷ 2)(x² ÷ x)
12x *Answer

Given f(x) = 14x³ and g(x) = 7x, find (f ÷ g)(x).
Solution:
(f ÷ g)(x) = f(x) ÷ g(x)
Divide the first equation by the second equation.
(14x³) ÷ (7x)
(14 ÷ 7)(x³ ÷ x)
2x² *Answer

Now you try:
Given f(x) = 6x - 4 and g(x) = 5x + 2
find (f + g)(x)
Enter your answer to check if you got it right.
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Now you try:
Given f(x) = 3x + 5 and g(x) = -2x + 4
find (f - g)(x)
Enter your answer to check if you got it right.
Check Answer

Now you try:
Given f(x) = 5x - 1 and g(x) = 3x + 7
find (f・g)(x)
Enter your answer to check if you got it right.
Use the caret key (^) to enter exponents.
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Now you try:
Given f(x) = 36x⁴ and g(x) = 3x²
find (f ÷ g)(x)
Enter your answer to check if you got it right.
Use the caret key (^) to enter exponents.
Check Answer