Rewriting a function with y as the independent variable

In summary, The conversation discusses solving quadratic equations and finding x in terms of y. However, it is noted that this may not always be possible, as with the example of y=x+sin(x).
  • #1
Sidthewall
33
0
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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  • #2
It's just a quadratic in x where you treat y as a constant.
[tex]y=x^2-x[/tex]

[tex]x^2-x-y=0[/tex]
 
  • #3
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
 
  • #4
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).
 
  • #5
Yep Mute's got it :tongue:
 

What does it mean to rewrite a function with y as the independent variable?

Rewriting a function with y as the independent variable means to rearrange the equation so that y is on the left side and all other variables are on the right side. This allows us to solve for y and find the relationship between y and the other variables.

Why would you want to rewrite a function with y as the independent variable?

Rewriting a function with y as the independent variable can make it easier to graph and analyze the relationship between y and the other variables. It can also help to identify patterns and make predictions about the behavior of the function.

What are the steps for rewriting a function with y as the independent variable?

The steps for rewriting a function with y as the independent variable vary depending on the original equation, but generally involve isolating y on one side of the equation, simplifying both sides, and then rearranging to solve for y.

Can you provide an example of rewriting a function with y as the independent variable?

Yes, for example, if we have the function x = 3y + 2, we can rewrite it as y = (x - 2)/3 by subtracting 2 from both sides and then dividing by 3.

Are there any restrictions or limitations when rewriting a function with y as the independent variable?

Yes, there may be restrictions or limitations when rewriting a function with y as the independent variable, such as certain values or operations that are not allowed. It is important to check for these restrictions and make sure the rewritten function is valid for all possible values of the variables.

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