yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Difference of functions | Functions and their graphs | Algebra II | Khan Academy


2m read
·Nov 11, 2024

We're told that f of x is equal to two x times the square root of five minus four, and we're also told that g of x is equal to x squared plus two x times the square root of five minus one. They want us to find g minus f of x, so pause this video and see if you can work through that on your own.

The key here is to just realize what this notation means: g minus f of x is the same thing as g of x minus f of x. And so again, if this was helpful to you, once again I encourage you to pause the video.

All right, now let's work through this again. This is going, or I guess the first time, but now that we know that this is equal to g of x minus f of x, so what is g of x? Well, that's the same thing as x squared plus 2x times the square root of 5 minus 1.

And what is f of x? Well, it's going to be 2 x times the square root of 5 minus 4. We are subtracting f of x from g of x, so let's subtract f of x from g of x. Now it's just going to be a little bit of algebraic simplification.

This is going to be equal to x squared plus 2x times the square root of 5 minus 1. Now we just have to distribute this negative sign. So negative 1 times 2x times the square root of 5 is going to give us minus 2x times the square root of 5.

Then the negative of negative 4 is positive 4. Let's see if we can simplify this sum. We only have one x squared term, so that's that one there. So we have x squared, and let's say we have 2x times the square root of 5, and then we have another, oh, now we subtract 2x times the square root of 5.

So these two cancel out with each other, so those cancel out, and then we have minus 1 plus 4. If we have negative 1 and then we add 4 to it, we're going to have positive 3.

So if we just factor this and take this into consideration, four minus one is going to be equal to three. And we're done! That's what g minus f of x is equal to: x squared plus three.

More Articles

View All
Limits at infinity of quotients with square roots (even power) | AP Calculus AB | Khan Academy
Let’s see if we can find the limit as x approaches negative infinity of the square root of four x to the fourth minus x over two x squared plus three. And like always, pause this video and see if you can figure it out. Well, whenever we’re trying to find…
Formula 1 Driver's INSANE Watch | First Time Reviewing H.Moser & Cie
This is craftsmanship. This is what we love in Swiss traditional watchmaking. What a dial! It just explodes! Smoky hot, it’s beautiful. Good [Music]. Question: this is wonderful. Here with a story of a rather unique brand, it’s H. Moser, but everybody ju…
The Problem With Rich People
Pick up to the sound of the alarm on your iPhone, and annoyed that you couldn’t get more sleep, you grudgingly unlock your phone to see what’s going on in the world. There’s an email from Amazon telling you that your package has been delivered. So, you fo…
Unleashing the Power of the Mind Through Neuralink #Shorts
Each near-link N1 chip is roughly 4x4 millimeters with a thousand electrodes each. It’s feasible to fit up to 10 of these inside your head in different areas, all to measure and affect different parts of your brain. Using just 256 electrodes, or about two…
Associative and commutative properties of addition with negatives | 7th grade | Khan Academy
What we’re going to do in this video is evaluate this pretty hairy expression. We could just try to do it; we could go from left to right, but it feels like there might be a simpler way to do it. I’m adding 13 here, and then I’m subtracting 13. I have a n…
Mild and medium tension | Forces and Newton's laws of motion | Physics | Khan Academy
You bought a huge canister aluminum can of super hot red peppers, 3 Kg worth, and you hung them from two strings from the ceiling ‘cause you don’t want anyone to get your super hot red peppers. You wanted to know what’s the tension in both of these string…