# Rewriting a function with y as the independent variable

1. Aug 18, 2010

### Sidthewall

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 plz

2. Aug 18, 2010

### Mentallic

It's just a quadratic in x where you treat y as a constant.
$$y=x^2-x$$

$$x^2-x-y=0$$

3. Aug 18, 2010

### Sidthewall

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. Aug 18, 2010

### Mute

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. Aug 18, 2010

### Mentallic

Yep Mute's got it :tongue:

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