Is x=y^2 a One to One Function?

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The discussion centers on the mathematical properties of the equations y = x² and x = y², specifically regarding their classification as one-to-one functions. It is established that y = x² is not a one-to-one function due to the existence of multiple y values for a single x value. Conversely, x = y² also fails the one-to-one criterion, as it can be rewritten as y = ±√x, resulting in two y values for most x values in its domain. Therefore, both functions are confirmed to be non-one-to-one.

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Hepic
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I want to make one question. I know that function with that equation: y=x^2 is not one to one.
What about x=y^2 ??

It is one to one or nope??(I know what means one by one,but I am a bit confused,answering in my question,everything will be clear.)
Thanks!
 
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Are you asking about x as a function of y, or is y intended to still be a function of x? If x is a function of y, then it is still the case that if I plug in y or -y, I get the same value of x, so it's not one to one. If y is supposed to be a function of x then you haven't actually defined a function, as given an x value there are multiple y values that could work.
 
I just ask if this function:y=x^2 is one to one.
 
Hepic said:
I just ask if this function:y=x^2 is one to one.

In your original entry you said you know it is not. What is your question? Simply moving letters around does not make it any clearer.
 
Sorry,that was my wrong.
By the way both functions(y=x^2 and x=y^2) are one to one,or no?
 
You had it right in your first post -- y = x2 is NOT a one-to-one function.

For x = y2, the answer depends on whether x is the dependent variable or y is.

If x is the dependent variable (i.e., x is a function of y), then the graph of x = y2 looks just like the graph of y = 2, but the first graph has the axes labeled differently.

If x is the independent variable, then the equation x = y2 can be rewritten as y = ±√x. Since there are two y values for most x values in the domain, this isn't even a function, let alone a one-to-one function.
 
You have already been told, it is NOT a function.
 
Hepic said:
http://www.mathwarehouse.com/geometry/parabola/images/x=y2_vertical_line_test.gif

This function is one by one?
The image you posted could be clearer if the two axes were labeled. From the graph and the equation, the vertical axis has to be the y-axis, and the horizontal axis has to be the x-axis.

The image shows a vertical red line, so wherever you got this was probably showing an example of using the vertical line test. What does your book (or wherever you got this image) say about a graph for which a vertical line intersects two or more points?
 
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The question has been asked and answered, so I'm closing this thread.
 

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