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

  • Thread starter Thread starter Hepic
  • Start date Start date
  • Tags Tags
    Function
AI Thread Summary
The discussion clarifies that the function x = y^2 is not one-to-one, as it can yield multiple y values for a single x value. When x is treated as a function of y, the equation does not satisfy the definition of a function because it fails the vertical line test. Conversely, y = x^2 is also confirmed to be not one-to-one for similar reasons. The confusion arises from the interpretation of the variables, but ultimately both equations do not represent one-to-one functions. The thread concludes that the question has been adequately answered, and further discussion is unnecessary.
Hepic
Messages
118
Reaction score
0
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!
 
Mathematics news on Phys.org
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?
 
  • #10
The question has been asked and answered, so I'm closing this thread.
 

Similar threads

I My attempt to understand horizontal transformations of functions
Replies
6
Views
1K
I What are the applications of inverses of vector functions?
Replies
17
Views
3K
I Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
Replies
3
Views
1K
B Analyzing y as a Function of x
Replies
19
Views
2K
B Can We Simplify the Taylor Series Expansion for e^(f(x,y))?
Replies
3
Views
2K
MHB Which Quadratic Function Has Exactly One X-Intercept?
Replies
3
Views
2K
MHB Finding minimum value of function with two variable
Replies
7
Views
2K
B Difference between functions and variables
Replies
13
Views
2K
MHB Is $f(x) = xf(1)$ the only solution to the given functional equation?
Replies
3
Views
1K
B Why Do Functions Have Only One Output for Each Input?
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top