What Are Implicit Functions and Ordered Pairs in Algebra?

[gabby989062]

Homework Statement

Find two functions defined implicitly by the relation 9y^2=x^2
$$9y^{2}=x^{2}$$


2. Find three ordered pairs in the relation xy=12

The Attempt at a Solution

1. my attempt is $$f(x)= \sqrt{9y^{2}}$$

and

$$f(y)=\sqrt{\frac{x^{2}}{9}}$$
So...is this the right way to do this question?
am i allowed to put a f() around my x and y and then solve for x and y?


2. I guess it would be either (2,6) OR (3,4) OR (1,12)
Is this correct and what the heck is an ordered pair?

 

[berkeman]

I think you are on the right track. The two relations would be f(x) and f(y), I think. And solving for the ordered pairs (x,y) would be along the lines you suggest.

 

[gabby989062]

Thanks you!.

 

[learningphysics]

If 9y^2=x^2 and you solve for y, what do you get?

y = $$\pm\frac{x}{3}$$

The y is the result of the function... ie f(x), g(x) etc...

So the two functions implicit here are:

f(x) = x/3 and g(x) = -x/3