Question

Determine if the function is even, odd or neither f(x)=x/(x2−1)

Answer 1

Replace x by -x, then simplify.

1) Is the resulting equal to the same function f(x)? (Then it is odd.)
2) Is the resulting function equal to its negative, \(f(x)=-\frac{x}{x^2-1}\)? (Then it is odd.)
3) If it satisfies neither of the two steps above, then the answer is neiter.

Answer 2

can you show me how this question is done @Jnlucero ??

Answer 3

Sure. :)

Answer 4

Thanks

Answer 5

f(-x) = (-x)/[(-x)^2-1]=-x/(x^2-1), since (-x)^2=x^2.

Now notice that the resulting function equals its negative. That is, f(-x)=-f(x). Thus the function is odd. :) (PS: Why is the equation editor not working here?)

Answer 6

How about this ?? f(x)=x^6+8x^2

Answer 7

@Jnlucero

Answer 8

f(-x)=(-x)^6+8(-x)^2=x^6+8x^2 (the same function)

Answer 9

the one before this question, the function is odd but theres not (-) infront x^2

Answer 10

@Jnlucero is the last question odd??

Answer 11

f(-x)=(-x)^6+8(-x)^2=x^6+8x^2 (the same function)

Answer 12

2nd to last question: However, there is (-) in front of the whole expression x/(x^2-1)=f(x).
Last question: It is the same function as f(x). So, it must be odd.

Answer 13

okay thanks

Answer 14

Last question, i mean its even.. (sorry. :/)

Answer 15

oh its fine

Answer 16

Thanks .:)