# Function Operations – Practice ProblemsHaving fun while studying, practice your skills by solving these exercises!

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A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range. Often functions are written in a form like f(x)=3x+5, where x is the element in the domain and 3x+5 gives the y which x is “sent to” in the range.

Functions can be combined using arithmetic operations which are similar to those used on polynomials: always combine like terms, remember the FOIL method, and don’t forget to simplify if the answer can be simplified! Here are some examples of performing operations with the functions f(x) = x² – 2x + 1 and g(x) = x – 1:

(f + g)(x) = f(x) + g(x)
= (x² – 2x + 1) + (x – 1)
= x² – 2x + x + 1 – 1
= x² – x

Subtract: f(x) – g(x)
(f – g)(x) = f(x) – g(x)
= (x² – 2x + 1) – (x – 1)
= x² – 2x – x + 1 + 1
= x² – 3x + 2

Multiply: f(x) ∙ g(x)
(f ∙ g)(x) = f(x) ∙ g(x)
= (x² – 2x + 1) (x + 1)
= x³ – 2x² + x² + x – 2x + 1
= x³ – x² – x + 1

Divide: f(x) ÷ g(x)
(f ÷ g)(x) = f(x) ÷ g(x)
= (x² – 2x + 1) ÷ (x – 1)
= [(x – 1)(x – 1)] ÷ (x – 1)
= x – 1

We need to perform operations on functions to calculate the change of temperature, compare production rates of companies, create phone apps, and so much more.

This lesson is also a prerequisite for studying composite functions.

Build a function that models a relationship between two quantities.
CCSS.MATH.CONTENT.HSF.BF.A.1.B

Exercises in this Practice Problem
 Determine the total cost of the sand-proof glass carpet dome. Establish the equation to calculate Jaanav total profit. Examine the total cost of the production with Janaav's brother's new glass dome machine. Figure out the price for one dome. Decide what the correct rules are for combining functions. Calculate each operation with the given functions.