It was sweet going through precalculus for the first time and using this to derive an equation to convert radians to degrees along with it's inversion just by knowing 180 deg = pi. Your content is seriously second to none.
This will occur with any function where x+y= constant like in this case, 7. You may know already that the inverse of a function can be visualized as a reflection in the line y=x . In this case, you can imagine that (5,2) will map to (2,5). So in a sense, it flips onto itself across the y=x line but ends up being the "same" function. The "x" input you are talking about in the inverse function however is the "y" that you got from the original function.
Pretty sure that's right. I thought Leonard would point that out to the class. Was kinda surprised when he didn't. Now I'm questioning my sanity. -x+7 IS the same thing as 7-x, right? Right?? RIGHT!?!?!!??? Aaaaaaaaagghghghghghgghghghghgghghg!!!! NEED ANSWER. LOSING MIND. Iä! Iä! Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!
First 10 minutes, should be "every output has a unique input", not the other way around. An understandable slip-up, but an important distinction that might be confusing.
@@crystyxn When you say "every input has a unique output", that's just the definition of a function. For example, y = x^2 is the squaring function. Every input x has a unique output y. x = 2 --> y = 4; x = 5 -> y = 25; x = pi --> y = pi^2. Every number only has one square. But when you say "every output has a unique input", that's saying it's 1-1. The squaring function is not 1-1, because NOT every output has a unique input. y = 9 has two inputs, x = 3 and x = -3, since both 3^2 and (-3)^2 equal 9. x = 3 --> y = 9, but also x = -3 --> y = 9. So, the output y = 9 does not have a unique input, it has TWO inputs. So, the squaring function is not invertible.
@@DarinBrownSJDCMath But by the definition of "unique" it kinda makes sense this way too. Both the inputs of 3 and -3 have the outputs of 9, so they don't have "unique" outputs (i.e some other input has the same output, hence the output is not unique), so the function is not 1-to-1. I get what you mean but it make sense this way too, at least language-wise, I think. Please clear it up for me if I'm wrong because english is not my first language
@@alex-ie8tp Yes, I see what you're saying, but that's not what the language means. When outputs are said to be unique, it's in reference to a particular input, and vice versa.
Function y = x^2 is not a one to one function. eg : For 2 different values of x (1.-1), we get the same y = 1. Hence this function doesn't have inverse.
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It was sweet going through precalculus for the first time and using this to derive an equation to convert radians to degrees along with it's inversion just by knowing 180 deg = pi. Your content is seriously second to none.
You're talented at making ambiguous concepts make a lot of sense! thanks!
38:22 student expressing his frustration with functions lol; "...fuck."
This is the best explanation I have ever seen for inverse functions. Great work!!
If it wasn't because of this video I wouldn't be able to understand inverse functions. You have a talent, your students are lucky!! Thanks.
Epic lesson as always!!
For f(x) = 7-x you get the answer f-1(x)=-x+7 can’t that be rewritten as f-1(x)=7-x meaning the inverse is the same as the original function?
Yeah, this really broke my mind too. Help us Professor Leonard, you're our only hope.
This will occur with any function where x+y= constant like in this case, 7. You may know already that the inverse of a function can be visualized as a reflection in the line y=x . In this case, you can imagine that (5,2) will map to (2,5). So in a sense, it flips onto itself across the y=x line but ends up being the "same" function. The "x" input you are talking about in the inverse function however is the "y" that you got from the original function.
Pretty sure that's right. I thought Leonard would point that out to the class. Was kinda surprised when he didn't. Now I'm questioning my sanity. -x+7 IS the same thing as 7-x, right? Right?? RIGHT!?!?!!??? Aaaaaaaaagghghghghghgghghghghgghghg!!!! NEED ANSWER. LOSING MIND. Iä! Iä! Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!
38:22 ..."fuck" lmao
xD
First 10 minutes, should be "every output has a unique input", not the other way around. An understandable slip-up, but an important distinction that might be confusing.
whats the difference? could you give some examples?
@@crystyxn When you say "every input has a unique output", that's just the definition of a function. For example, y = x^2 is the squaring function. Every input x has a unique output y. x = 2 --> y = 4; x = 5 -> y = 25; x = pi --> y = pi^2. Every number only has one square. But when you say "every output has a unique input", that's saying it's 1-1. The squaring function is not 1-1, because NOT every output has a unique input. y = 9 has two inputs, x = 3 and x = -3, since both 3^2 and (-3)^2 equal 9. x = 3 --> y = 9, but also x = -3 --> y = 9. So, the output y = 9 does not have a unique input, it has TWO inputs. So, the squaring function is not invertible.
@@DarinBrownSJDCMath Thanks for the clear up!
@@DarinBrownSJDCMath But by the definition of "unique" it kinda makes sense this way too. Both the inputs of 3 and -3 have the outputs of 9, so they don't have "unique" outputs (i.e some other input has the same output, hence the output is not unique), so the function is not 1-to-1. I get what you mean but it make sense this way too, at least language-wise, I think. Please clear it up for me if I'm wrong because english is not my first language
@@alex-ie8tp Yes, I see what you're saying, but that's not what the language means. When outputs are said to be unique, it's in reference to a particular input, and vice versa.
Thank you professor
Very well explained!
Brilliant.
THANKS!!!
you are amazing!
38:22
I saw how you put +6 for the x and the Y so you didnt had to add them?
EPIC GUY
What about inverse of x^2 it is sqrt of x that is not a reflection in a diagonal line.
Function y = x^2 is not a one to one function.
eg : For 2 different values of x (1.-1), we get the same y = 1.
Hence this function doesn't have inverse.
Even i was also going to tell him the same answer🙄🙄😂😂