Rewriting a function with y as the independent variable

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Discussion Overview

The discussion revolves around rearranging equations to express x as a function of y, particularly focusing on the quadratic equation y = x^2 - x. Participants explore the challenges of solving for x when multiple x variables with different exponents are involved.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents the equation y = x^2 - x and seeks to rearrange it to express x in terms of y, noting difficulties with equations involving multiple x variables with different exponents.
  • Another participant suggests treating y as a constant and reformulating the equation into a standard quadratic form, indicating that it can be solved for x.
  • A later reply emphasizes that while it is possible to solve for x in this case, it may not always be feasible for other functions, such as y = x + sin(x), where explicit solutions for x in terms of y may not exist.
  • One participant acknowledges the previous contributions and agrees with the approach suggested by another participant.

Areas of Agreement / Disagreement

Participants express differing views on the ability to rearrange equations to solve for x in terms of y, with some agreeing that it can be done for certain quadratic forms while others highlight the limitations in more complex functions.

Contextual Notes

There are unresolved assumptions regarding the types of functions that can be rearranged and the conditions under which explicit solutions for x can be obtained.

Who May Find This Useful

Readers interested in algebraic manipulation of equations, particularly those involving quadratics and the relationship between dependent and independent variables.

Sidthewall
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Ok. Sooo. Let's say u have y=x+5. Then u know y-5=x. Now if u have y=x^2 - x. How would u rearrange it to find out what x equals. I found out that in general I cannot rearrange ewquatioms with mitiplr x variables with different exponents. So help me please
 
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It's just a quadratic in x where you treat y as a constant.
y=x^2-x

x^2-x-y=0
 
I am not trying to find the x-intercept. I need the function to have x as the dependent variable and y as the independent variable for ex. If y=sqr(25-x) then y^2 - 25 = -x
 
Sidthewall said:
I am not trying to find the x-intercept. I need the function to have x as the dependent variable and y as the independent variable for ex. If y=sqr(25-x) then y^2 - 25 = -x

Mentallic is pointing out that you have a quadratic equation of the form ax^2 + bx + c = 0. Solve the quadratic equation and you will get x in terms of y. (But there will be more than one solution as y = x^2 -x is not a 1 to 1 function).

Also, although you can do it in this case, note that you can't always explicitly solve for x in terms of y. For example, y = x + sin(x).
 
Yep Mute's got it :-p
 

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