# Combining Functions

♦Perform arithmetic ope rations on functions
♦Perform composition of functions

## Five Ways of Combining two functions f and g

 •Addition • Subtraction •Multiplication • Division •Composition

## Definitions

If f(x) and g(x) both exist, the sum , difference , product , quotient and composition of two functions f and g are defined by

Examples of Evaluating Combinations of Functions –Using Symbolic Representations

## Example of Addition of Functions :

Let f(x) = x^2 + 2xand g(x) = 3x-1

Find the symbolic re presentation for the function f + g and use this to evaluate (f + g)(2)

or Evaluate each function, then combine

## Example of Multiplication of Functions :

Let f(x) = x^2 + 2xand g(x) = 3x−1

Find the symbolic representation for the function fg and use this to evaluate (fg)(2)

Or

## Example of Composition of Functions:

Let f(x) = x^2 + 2xand g(x) = 3x-1

Find the symbolic representation for the function and use this to evaluate ()(2)

## Example of Composition of Functions:

Let f(x) = x^2 + 2xand g(x) = 3x-1

Find the symbolic representation for the function and use this to evaluate ()(2)

Example:

Let f(x) = 1-5x and

Find

Find

Example: Composition from tabular displays for functions.

Find ()(1)
Find
Find

## Evaluating Combinations of Functions Numerically

•Given numerical representations for f and and g in the table

•Evaluate combinations of f and and g as specified.

Examples:

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of July 21st you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

 "It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..." C. Sievert, KY

 Sofmath 19179 Blanco #105-234San Antonio, TX 78258 Phone: (512) 788-5675Fax: (512) 519-1805