Question

y=x√(1-x²)

Domain?

y=x(1-x²)^(1/2)
y=x/[(1-x²)^(-2)]?

x≠±1

Symmetry?
f(3)=192
f(-3)=-300
-f(-3)=300
no symmetry?

Answer 1

For your domain you may only have

-1 < x < +1

Suppose x = 5
then y = 5/√-24 which is undefined.
You only considered when the denominator is zero.

BTW, how did you get those f(x) values,
e.g. f(3) = 192
I get f(3) = 3/√-8

Answer 2

Then isn't the domain -1≤x≤1, since when I plug in -1 and 1, the answer is 0.
For symmetry, I plugged 3 into y=x/[(1-x²)^(-2)], which I'm guessing is wrong. Since domain is -1≤x≤1, I switched the number to 0.5, and found that it is symmetrical about the origin.

Thank you!

Answer 3

Yes, you are right, I should have used the
≤ symbol.
And yes, there is symmetry about the origin.