Inequality of function with two variable: book sugestion.

[danielvnl]

Can anyone suggest me a book that broach the subject, "Inequality of function with two variables" ? Especially one with many exercises (even if it's a high school book).
I need it because I'm trying to find the domain of functions with several variables on calculus, but my high school graduation wasn't that good. So I'm very newbie about this subject.

Thank you all.

 

[stapel]

Wouldn't any algebra textbook cover this topic? Perhaps you could provide an example of what you're talking about? Thank you!

 

[danielvnl]

Okay. For instance

1- Find the domain of the function F(x,y)=sqrt(|x|+|y|).
2- Find the domain of the function F(x,y)=(xy)/[(sqrt(x^2-y^2)]
2- Solve the inequality (x-y)>0

I want o book that broach these content with some exercises like that.

I think analytic geometry approach this well, but I'm not finding this kind of book.

 

[stapel]

1- Find the domain of the function F(x,y)=sqrt(|x|+|y|).
2- Find the domain of the function F(x,y)=(xy)/[(sqrt(x^2-y^2)]
2- Solve the inequality (x-y)>0

I want o book that broach these content with some exercises like that.

I think analytic geometry approach this well, but I'm not finding this kind of book.

Analytical geometry is part of algebra, so algebra books will cover much of this. ("Pre-calculus", "Algebra II", "Intermediate" or "Advanced" algebra books, by the way; "pre-algebra" or "Beginning" algebra books may not get far enough.) To be fair, most algebra books won't cover functions of two variables, though. (By "function with two variables", I'd thought you'd meant something like "y = f(x)".)

To learn how to find domains of basic one-variable functions, try here. To learn how to find domains of two-variable functions, try here. To learn how to solve (that is, to find the graph of) linear inequalities, try here.

 

[HallsofIvy]

The domain of $\displaystyle \sqrt{x}$ is "x non-negative".

Since |x| and |y| are never negative, neither is |x|+ |y|.

In the second problem, for the same reason, we must have $\displaystyle x^2- y^2\ge 0$.
The simplest way to solve an inequality with two variables is to solve the associated equality. The point is that a continuous function can go from ">" to "<" or vice versa only where it is "=". So what x and y satisfy $\displaystyle x^2- y^2= 0$? What points in the xy-plane are they. (Of course $\displaystyle x^2- y^2= (x- y)(x+ y)$ makes that easy.) Then determine in which of the regions, bounded by that graph, do we have "> 0" and in which "< 0".

For the third problem if x- y> 0 then x> y. Again, the simplest way to do that is to graph the line x- y= 0 or y= x. On one side of that line x-y> 0, on the other x- y< 0.

 

[danielvnl]

Analytical geometry is part of algebra, so algebra books will cover much of this. ("Pre-calculus", "Algebra II", "Intermediate" or "Advanced" algebra books, by the way; "pre-algebra" or "Beginning" algebra books may not get far enough.) To be fair, most algebra books won't cover functions of two variables, though. (By "function with two variables", I'd thought you'd meant something like "y = f(x)".)

To learn how to find domains of basic one-variable functions, try here. To learn how to find domains of two-variable functions, try here. To learn how to solve (that is, to find the graph of) linear inequalities, try here.

Thank you so much stapel, I found an algebra college book that cover linear equations and inequalities in two variables, but it don't cover nonlinear functions in two variables, like logarithms or exponencial functions. But I'm on the right way, I'll keep trying to find others.

Thank you so much.