Rewriting a function with y as the independent variable

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To rearrange the equation y = x^2 - x to express x in terms of y, one can rewrite it as x^2 - x - y = 0, which is a quadratic equation. Solving this quadratic will yield multiple solutions for x due to the nature of the function not being one-to-one. It's important to note that not all equations can be rearranged to isolate x in terms of y, as seen in the example y = x + sin(x). The discussion emphasizes the need to treat y as a constant when solving for x. Understanding these principles is crucial for effectively manipulating equations with multiple 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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