Free Algebra Tutorials!

 Home Point Arithmetic Operations with Numerical Fractions Multiplying a Polynomial by a Monomial Solving Linear Equation Solving Linear Equations Solving Inequalities Solving Compound Inequalities Solving Systems of Equations Using Substitution Simplifying Fractions 3 Factoring quadratics Special Products Writing Fractions as Percents Using Patterns to Multiply Two Binomials Adding and Subtracting Fractions Solving Linear Inequalities Adding Fractions Solving Systems of Equations - Exponential Functions Integer Exponents Example 6 Dividing Monomials Multiplication can Increase or Decrease a Number Graphing Horizontal Lines Simplification of Expressions Containing only Monomials Decimal Numbers Negative Numbers Factoring Subtracting Polynomials Adding and Subtracting Fractions Powers of i Multiplying and Dividing Fractions Simplifying Complex Fractions Finding the Coordinates of a Point Fractions and Decimals Rational Expressions Solving Equations by Factoring Slope of a Line Percent Introduced Reducing Rational Expressions to Lowest Terms The Hyperbola Standard Form for the Equation of a Line Multiplication by 75 Solving Quadratic Equations Using the Quadratic Formula Raising a Product to a Power Solving Equations with Log Terms on Each Side Monomial Factors Solving Inequalities with Fractions and Parentheses Division Property of Square and Cube Roots Multiplying Two Numbers Close to but less than 100 Solving Absolute Value Inequalities Equations of Circles Percents and Decimals Integral Exponents Linear Equations - Positive and Negative Slopes Multiplying Radicals Factoring Special Quadratic Polynomials Simplifying Rational Expressions Adding and Subtracting Unlike Fractions Graphuing Linear Inequalities Linear Functions Solving Quadratic Equations by Using the Quadratic Formula Adding and Subtracting Polynomials Adding and Subtracting Functions Basic Algebraic Operations and Simplification Simplifying Complex Fractions Axis of Symmetry and Vertices Factoring Polynomials with Four Terms Evaluation of Simple Formulas Graphing Systems of Equations Scientific Notation Lines and Equations Horizontal and Vertical Lines Solving Equations by Factoring Solving Systems of Linear Inequalities Adding and Subtracting Rational Expressions with Different Denominators Adding and Subtracting Fractions Solving Linear Equations Simple Trinomials as Products of Binomials Solving Nonlinear Equations by Factoring Solving System of Equations Exponential Functions Computing the Area of Circles The Standard Form of a Quadratic Equation The Discriminant Dividing Monomials Using the Quotient Rule Squaring a Difference Changing the Sign of an Exponent Adding Fractions Powers of Radical Expressions Steps for Solving Linear Equations Quadratic Expressions Complete Squares Fractions 1 Properties of Negative Exponents Factoring Perfect Square Trinomials Algebra Solving Quadratic Equations Using the Square Root Property Dividing Rational Expressions Quadratic Equations with Imaginary Solutions Factoring Trinomials Using Patterns
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Adding and Subtracting Functions

Recall that a function is a rule that assigns exactly one output number to each input number.

We can combine functions in several ways in order to make new functions.

Definion â€” Sum and Difference of Two Functions

Given two functions, f(x) and g(x):

The sum of f and g, written (f + g)(x), is defined as (f + g)(x) = f(x) + g(x).

The difference of f and g, written (f - g)(x), is defined as (f - g)(x) = f(x) - g(x).

The domains of (f + g)(x) and (f - g)(x) consist of all real numbers that are in the domain of both f(x) and g(x).

Example 1

Given f(x) = 0.5x + 4 and g(x) = 0.25x + 1, find the sum (f + g)(x).

Solution

 Use the definition for the sum of functions.Substitute for f(x) and g(x). Combine like terms. So, (f + g)(x) = 0.75x + 5. (f + g)(x) = f(x) + g(x) = (0.5x + 4) + (0.25x + 1) = 0.75x + 5

Example 2

Given f(x) = 5x2 + 6x - 12 and g(x) = 8x - 15, find the difference (f - g)(x).

Solution

 Use the definition for the difference of functions. Substitute for f(x) and g(x). Remove parentheses. Combine like terms. (f - g)(x) = f(x) - g(x) = (5x2 + 6x - 12) - (8x - 15) = 5x2 + 6x - 12 - 8x + 15 = 5x2 - 2x + 3
So, (f - g)(x) = 5x2 - 2x + 3.

You have already learned to evaluate a function for a specific value of the input.

 For example, if f(x) = 2x + 1, then we can find f(3) by substituting 3 for x in the function rule. f(x) f(3) = 2x + 1 = 2(3) + 1 = 7
Likewise, we can evaluate the sum or difference of two functions for a given number. There are two methods that are typically used.

Procedure â€” To Evaluate the Sum or Difference of Functions

Step 1 Find (f + g)(x) or (f - g)(x).

Step 2 Use x = a to find (f + g)(a) or (f - g)(a).

All Right Reserved. Copyright 2005-2023