@EddieWoo thank you for a wonderful explanation, however I have a question: when we restrict the domain of the regular function to x >= 0, we get the inverse function sqrt of x, why can't we restrict the domain of the function to x
great lectures, but will say that the reason sqrt of x doesnt have a fully symmetric graph like x^2 is because the sqrt of x cannot return negative real numbers (only i values). The way he says it kinda implies that humans restrict the function by convention
I think there is a misconception here maybe. From my point of view, we must differenciate the domain of x and the range of f(x). x cannot be negative because taking the square root of a negative number would involve finding a number that, when squared, gives a negative result, and that concept doesn't have a real-number solution in the standard mathematical framework. So, x cannot be a negative number. BUT, even if we cannot find any image of srqt(-4) for instance, this is not the reason why we remove the downside of the function graphically. It is not by restricting the domain, but by restricting the range. Because sqrt(4) is -2 and +2, we could, even with positive values of x, having two values of f(x). I have not finished yet the video of professor Eddie Woo, but we really do not restrict the domain of srqt(x), x>=0 is already the domain of the function f(x)=sqrt(x). What needs to be restricted is actually the range of the function, being R[0 ; +infinity[ instead of ]-infinity; +infinity[. Overall, it is therefore by human convention that we restrict the range in order to make sqrt(x) a function. Maybe someone could corroborate what I am talking about, because I am not confident enough to qualifying my thoughts to be the truth. EDIT: After consulting Quora forums, I fell into this topic that made me clearing everything. I think I was wrong. www.quora.com/Why-is-y-sqrt-x-a-function-if-square-roots-have-two-answers-positive-and-negative-and-a-function-can-only-have-one-output-per-input
It makes me happy that there are teachers this good in the world.
Why can't all the math teachers tie everything into a whole like this?! Thanks so much for filling in the holes for me!
Good lesson , you are a very good teacher, I saw one of your videos and now I'm more curious and I want to discover the world of mathematics :)
I never knew why negative root numbers were imaginary till now
@EddieWoo thank you for a wonderful explanation, however I have a question:
when we restrict the domain of the regular function to x >= 0, we get the inverse function sqrt of x, why can't we restrict the domain of the function to x
Composition of f and its inverse isn't necessarily cOmmutative though! Right 6:30
This was so helpful! Thanks for helping me understand
i love you for this.
great lectures, but will say that the reason sqrt of x doesnt have a fully symmetric graph like x^2 is because the sqrt of x cannot return negative real numbers (only i values). The way he says it kinda implies that humans restrict the function by convention
Why can't it though? I never really understood it. The square root of 4 should be both positive and negative 2, right?
I think there is a misconception here maybe. From my point of view, we must differenciate the domain of x and the range of f(x).
x cannot be negative because taking the square root of a negative number would involve finding a number that, when squared, gives a negative result, and that concept doesn't have a real-number solution in the standard mathematical framework.
So, x cannot be a negative number.
BUT, even if we cannot find any image of srqt(-4) for instance, this is not the reason why we remove the downside of the function graphically. It is not by restricting the domain, but by restricting the range.
Because sqrt(4) is -2 and +2, we could, even with positive values of x, having two values of f(x). I have not finished yet the video of professor Eddie Woo, but we really do not restrict the domain of srqt(x), x>=0 is already the domain of the function f(x)=sqrt(x). What needs to be restricted is actually the range of the function, being R[0 ; +infinity[ instead of ]-infinity; +infinity[.
Overall, it is therefore by human convention that we restrict the range in order to make sqrt(x) a function.
Maybe someone could corroborate what I am talking about, because I am not confident enough to qualifying my thoughts to be the truth.
EDIT: After consulting Quora forums, I fell into this topic that made me clearing everything. I think I was wrong.
www.quora.com/Why-is-y-sqrt-x-a-function-if-square-roots-have-two-answers-positive-and-negative-and-a-function-can-only-have-one-output-per-input
Bro this is Amazing
You are awesome!!!!!
You should have more subscribers than Vsauce
Where are all the missing subscribers?
avi12 only the positive ones got reflected over