- #1

cathal84

- 15

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## Homework Statement

f(x,y) = 1/y^2-x

find the domain of f.

Given c ∈ R \ {0} find (x, y) ∈ R 2 such that f(x, y) = c. Finally determine the range of f.

## Homework Equations

I know that the domain of the function is anywhere that the function is defined.

## The Attempt at a Solution

in the case of this question i can see that the function is going to be undefined where y^2-x =0

since anything over 0 is undefined.

I believe that for the range part of the question it is essentially saying, define the range such that x and y are real numbers but please correct me if I'm wrong.

When i used to be dealing with functions such as f(x) = x+1, in that case i knew that the domain was where the function was defined over the x-axis and i knew that the range was where the function was defined over the y-axis.

But since the domain now is including X and Y i have no idea by what they mean by finding the range.

So if someone could help me define the range of this function and show me the steps to defining the range of any other multi-variable like this one i would greatly appreciate it!

This question is purely for study purposes for exam in start of January so feel free to go into as much detail as you want if you feel it would aid understanding. Thanks again!

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