Can you please check my answers for these questions:?

Question

1. y=x³=odd
2. y=x+2=neither
3. y=x²-3=neither
4. y= (1)/(x²-1)=even
5. y= (x)/(x²-1)=even
6. y=X^4=even
7. y=x+x²=odd
8. y=x+x³=odd
9. y=(1)/(x-1)=neither
10. y= (x²)/(x²-1)=even
Please tell me if it is correct or not!

Answer 1

(3): y = x^2 - 3 is even
(5): y = x / (x^2 - 1) is odd
(7): y = x + x^2 is neither.
All the others are correct.

For (3): replace x by -x, we get y = (-x)^2 - 3 = x^2 - 3, the same as the original function, so it is even.

For (5): replace x by -x, we get y = (-x) / ((-x)^2 - 1) = -x / (x^2 -1 ), the negative of the original function, so it is odd.

For (7): replace x by -x, we get y = -x + (-x)^2 = -x + x^2 which is neither the same as x + x^2 or -(x + x^2). So it is neither odd nor even.