Solving Operations on Functions:
Okay, before you start reading this, you should know the basics on polynomials. That means you should know how to add, subtract, multiply, and divide polynomials. In this article, I will be teaching you how to also add, subtract, multiply, and divide functions. Solving Operations on Functions is a relatively easy method. This article will show exactly how to solve operations on functions.
Solving Operations on functions should not be difficult learn. It just means that when you have formulas for two functions, and need to find the sum, all you need to do is add the two formulas. Other than that, that is all you will need to do. Well, you might have to simplify the expressions, but that is a more complicated problem that I won’t be going over with in this article.
Are you ready to dive in?
I sure hope so. This lesson will be fun and short and you will walk away knowing all about operations on functions. You got this!
Let’s Look at Some Problems:
Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).
To find the answers, all you have to do is apply the operations: plus, minus, times, and divide.
Step 1: (f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
STEP 2: (f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
STEP 3: (f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15×2 – 10x
= –15×2 + 2x + 8
STEP 4: (f/g)(x)=f(x)/g(x)
That’s it for “operations on functions.” Don’t let the notation for this lesson scare you! All you need to remember is: add, subtract, multiply, or divide; then simplify if necessary. See, it’s easy! You got this!