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More Lessons for Algebra, Math Worksheets

In this lesson, we will look at how functions can be added, subtracted, multiplied or divided. You may also want to look at the lesson on composite functions.

**Functions: Adding and Subtracting**

Examples:

1. f(x) = x^{2} + 3x

g(x) = 8x + 9

(f+g)(x) = f(x) + g(x) =

2. f(x) = x^{2} + 2x + 8

g(x) = 3x^{2} - x + 7

(f-g)(x) = f(x) - g(x) =

**Functions: Multiplying and Dividing**

Example:

f(x) = (x^{2} - 1)

g(x) = (x + 1)

(fg)(x) =

(f/g)(x) =

**Combining Functions by Addition Subtraction Multiplication and Division**

Example:

f(x) = 3x^{2} + 4

g(x) = x - 5

(f + g)(x) =

(f - g)(x) =

(fg)(x) =

(f/g)(x) =

**Sum, Difference, Product and Quotient of Two Functions **

How to find the sum, difference, product and quotient of two functions and determine the domain?

Example:

f(x) = 5x - 4

g(x) = -9x + 6

(f + g)(x) =

(f - g)(x) =

(fg)(x) =

(f/g)(x) =

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra, Math Worksheets

Functions can be added.

**Example **

Add the functions f(*x*) = *x* + 2 and g(*x*) = 5*x* – 6

**Solution:**

(f + g)(*x*)

= f(*x*) + g(*x*)

= (*x* + 2) + (5*x* – 6)

= 6*x* – 4

Functions can be subtracted

**Example:**

Given f(*x*) = *x* + 2 and g(*x*) = 5*x* – 6, find (f – g)(*x*)

**Solution:**

(f – g)(*x*)

= f(*x*) – g(*x*)

= (*x* + 2) – (5*x* – 6)

= –4*x* + 8

Functions can be multiplied.

**Example:**

Add the functions f(*x*) = *x* + 2 and g(*x*) = 5*x* – 6

**Solution:**

(f • g)(*x*)

= f(*x*) • g(*x*)

= (*x* + 2)(5*x* – 6)

= 5*x*^{2} + 4*x* – 12

Functions can be divided.

**Example:**

Given f(*x*) = *x* + 2 and g(*x*) = 5*x* – 6, find

**Solution:**

for g(*x*) ≠ 0

Examples:

1. f(x) = x

g(x) = 8x + 9

(f+g)(x) = f(x) + g(x) =

2. f(x) = x

g(x) = 3x

(f-g)(x) = f(x) - g(x) =

Example:

f(x) = (x

g(x) = (x + 1)

(fg)(x) =

(f/g)(x) =

Example:

f(x) = 3x

g(x) = x - 5

(f + g)(x) =

(f - g)(x) =

(fg)(x) =

(f/g)(x) =

How to find the sum, difference, product and quotient of two functions and determine the domain?

Example:

f(x) = 5x - 4

g(x) = -9x + 6

(f + g)(x) =

(f - g)(x) =

(fg)(x) =

(f/g)(x) =

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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