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### Course: Algebra (all content)>Unit 7

Lesson 14: Combining functions

# Subtracting functions

Given that f(x)=2x√5-4 and g(x)=x^2+2x√5-1, Sal finds (g-f)(x). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What does "the principle square root" mean? Sal wrote it normally as sqrt of 5, but I'm not sure what the "principle" means here, since I have always heard square roots read aloud as "square root of 5" or whatever number you're taking the square root of. Please help! Thank you.
• The principle root of a number is just the positive square root. Each number has 2 square roots. For instance, the square root of 36 could be either 6 or negative 6. The principle root is 6.
(1 vote)
• at Sal talks about the principle square root of 5. What is a principle root? Is there a vid on it.
• The principal square root is the positive square root. There are 2 different numbers that can be squared to make 5, +sqrt(5) and -sqrt(5). If you squared either, they would make positive 5.
• At , Sal refers to the square root 5 as the principle square root of 5. Why is this?
• A square root generally has two answers. A positive answer and a negative answer.

A square root is asking, "what number, times itself, gives me this number?" So the square root of 25 is asking, "What number, times itself, gives me 25?". Well... 5*5 gives me 25. However, -5 * -5 also gives me 25. Both are valid answers for the square root of 25.

In general, most of the time, you want a positive number as your answer to a square root. The positive possible answer is also known as the "principal square root". So the principal square root of 25 is 5.

Sal just wanted to make it clear that he is using the positive possible answer, and not the negative possible answer to the square root of 5
• i didnt understand any of it...'
• The principle root of a number is just the positive square root. Each number has 2 square roots.
• I don't get it. The video won't play for me. :(
• Check to make sure your computer could play a video.
I never have this problem on KA Website.
• I'm confuse with the "removing the pharanthesis" part:

On the video, if we're going to substitute g(x)-f(x) with its definition, it will become:
(x^2+2x√5-1) - (2x√5-4). To get rid of the parenthesis, we have to multiply an imaginary -1 to the exprission, 2x√5-4. So, -1(2x√5) = -2x√5 and -1(-4) = 4, right? But why does the video say that -1(-4) = 5?
• Hi! Good question. They do multiply by a -1 and that changes the numbers making a (-) a (+). So, that's why they removed the parenthesis. I don't know if this helps but I hope it does.
(1 vote)
• so I'm 12, and I'm new to this, so do not judge me just help me, but for some reason, this is what I did:

(x^2+2*√5-1)-(2x√5-4)
(x^2+2*0-1)-(2x*0-4)
(x^2-1)-(-4)
(x^2-5)
but the answer was x^2-3 what did I do wrong.
• First, you changed the expression. It should be:
(x^2+2x√5-1)-(2x√5-4)

Next - Where did you get the 0's from in your 2nd line? You can't change √5 into 0. They are not equal.

The correct way to work the problem is to distribute the minus sign that is in front of the 2nd set of parentheses. This minus is the same as -1 just like "-x" is the same as "-1x". Distributing the minus or -1 results in changing the signs of the terms inside the parentheses:
(x^2+2x√5-1)-1(2x√5-4) = x^2+2x√5-1-2x√5+4
Then, you combine like terms:
x^2+2x√5-1-2x√5+4 = x^2+(2x√5-2x√5)+(-1+4)
= x^2+3

You never applied the minus sign to the -4. Instead, you treated: "-(-4)" as just "-4".

Hope this helps.