Find A Function

[harpazo]

The product of two numbers is 32. Find a function that represents the sum of their squares.

Solution:

Let x and y represent the two numbers. The product means to multiply.

xy = 32

Let S = sum of the squares of x and y.

S = x^2 + y^2

Now, the book tells me that I should solve xy = 32 for y and then plug into S.

Question:

Why must we solve xy = 32 for y? Why not solve for x as an option?

Book's Answer:

S(x) = x^2 + (32/x)^2

This is correct if the original question stated to find a function that represents the sum of their squares as y in terms of x. It does that say that anywhere.

If I solve xy = 32 for x, I get x = 32/y.

So the function simply changes to S(y) = (32/y)^2 + y^2. What's wrong with my function expressed as x in terms of y?

 

[MarkFL]

Either is correct, and observe that the output is the same no matter what we choose to use as our independent variable. Your book is likely simply following the convention that \(x\) be used as the independent variable.

 

[harpazo]

Either is correct, and observe that the output is the same no matter what we choose to use as our independent variable. Your book is likely simply following the convention that \(x\) be used as the independent variable.

Sounds good to me. Thank you, Mark.