Introduction to function inverses | Functions and their graphs | Algebra II | Khan Academy

Introduction to Function Inverses

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[joymariearga]

its just amazing how this video is uploaded way back in 2010 but is still very useful today and will be for the years to come. Thank you Khan Academy!!

[KosovaWarrior]

Teachers in our school just complicate it as much as possible to mash our brains...but you Khan Academy are something that brought help to me and many other people...I am making progress in math only because of you and not because of my teachers...they are very bad, thank you, keep going.

[shreendawg]

why cant my schools just play your vids in classes???

[yonu]

Nice watching this 10 years later cause of corona🦠

[TasyaAdzkiya]

5:15 Additional notes from me: a variable is a "bucket" that can be any number based on its constraints and can be changed to any symbol, letter, or maybe shapes (it's basically anything distinct to be used to represent the "bucket") without changing the value of the expression.

Up until x = f inverse of y = (1/2)y - 2, y is useful to see where it's coming from: it's coming from the original equation y = f(x) = 2x + 4, we just solve for x in terms of y to map from the range back to the domain or to make the output as the input and vice versa (that is why it is called inverse function).

After we know where it's coming from, it's useful that at this point and onward, we change the symbol/variable from y to x to see the relationship between f inverse of y to f(x) or f of x. We can do that because we just change the symbol or the variable without changing the value. We could've change the y into a or b or anything, but we chose to change the y into x because we need to see the relationship between the f inverse of y and the f(x) or f of x.

• x = f inverse of y = (1/2)y - 2 change the letter y to X to see the correlation between this equation to f(x) (it's not going to change the value, it's the same as if you were to use star shapes to represent a variable and decide to change them to heart shapes)
• x = f inverse of X = (1/2)X -2

We now see the correlation between f inverse of X and f(x) or f of x. In fact, f inverse of X is derived from f(x).

Notice that it might be a little confusing since now, in the x or f inverse of X equation, the domain (input) and range (output) are represented by the same variable, they are just differentiated by means of capital letter and lowercase letter: x = f inverse of X (let us use capital X as the input and the lowercase x as the output to differentiate them) = (1/2)X - 2.

• The x (range or output) = f inverse of X (domain or input) is similar to the y (range or output) in y (range or output) = f(x) or f of x (domain or input).
• The X (domain or input) in x (range or output) = f inverse of X (domain or input) is similar to the x (domain or input) in y (range or output) = f(x) or f of x (domain or input).

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Got nothing but praise for this guy. He actually makes sense teaching math.

[MICHAELSMITH-ebbr]

This video was super helpful. Your ability to explain things makes it unbelievably easy to comprehend and conceptualize these otherwise confusing concepts. It's bizarre that I could spend about an hour in a class with an instructor going over this material and still left not knowing much more than I did at the beginning of that hour, yet I watch this video that's less than 10 minutes, and I totally get it now. However, what I can't wrap my brain around is how 69 individuals found this video unhelpful and gave it a thumbs down.

[streetpartying]

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[EatShanklish]

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[cboyslim]

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[stevenjames]

Jussst when I thought I had almost all of the basic algebra down. I'm halfway through differential calculus and realized I needed to re learn this :)

[Peacefulcrystalmoon]

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[snnacho]

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[khanacademy]

@chizzy555 Maybe some trades. I could imagine the inverse trig functions would be pretty useful if you're building something.

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coming here when my teacher fails (that means i'm always here)

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[pforrest]

i had a moment when i had to pause the video just to be like cuz I finally understood. learning over zoom has been terrible but this was so helpful

[yashaswikulshreshtha]

Dude, like literally YOU'RE THE BEST. Your videos are so intuitive. I love it, I have been after teachers to tell me what's inverse they would tell me it's opposite of what it does, I knew what they wanna say but i felt unsatisfied like it didn't make sense although I knew how to do it. But that part where you just told that question is there any way to get back to the x. After that why you solved for x made perfect sense....