Functions of Several Variables

[affirmative]

My question is mostly down to staggering ignorance of basic notation. I have been unable to find a straightforward answer anywhere - so I assume it must be pretty basic.

I have a function: $$f(x,y)=x^3+y^3-3x-12y+20$$

Given that I know a value of x, ie $$x=-1$$, how do I extract a value of y using this notation?

I know when $$f(x)=x^2$$ I can use substitute $$f(x)$$ with $$y$$, but I find myself stuck with what to substitute $$f(x,y)$$ with...

 

[Mark44]

In order to evaluate your f(x, y), you need two numbers. What you get out isn't a y value; it's a z value. To graph the function, you need three dimensions. If you know a z value and an x value, there's the possibility that you can solve for the value you don't know: y. For example, if you know that f(x, y) = 10 and that x = 1, you might be able to solve the equation 10 = 1^3 + y^3 -3(1) - 12y + 20 to get y.

Does that make sense?

 

[affirmative]

Yes, it actually does. Thank you Mark.