maths question on functions (1 Viewer)

[Aznmichael92]

hello all, i am not sure if this function is odd or even. Can you explain why it is which?

x/(x^2 - 1)

 

[lyounamu]

hello all, i am not sure if this function is odd or even. Can you explain why it is which?

x/(x^2 - 1)

The best way to see whether it is even or odd is to do the test like this:

if f(-x) = f(x), it is even
if f(-x) = -f(x), it is odd
if f(-x) =/= f(x) & -f(x), it is neither

f(x) = x/(x^2-1)
f(-x) = -x/((-x)^2-1)
= -x/((x^2-1)
= -f(x)
Therefore, the function is odd.

 

[Aznmichael92]

The best way to see whether it is even or odd is to do the test like this:

if f(-x) = f(x), it is even
if f(-x) = -f(x), it is odd
if f(-x) =/= f(x) & -f(x), it is neither

f(x) = x/(x^2-1)
f(-x) = -x/((-x)^2-1)
= -x/((x^2-1)
= -f(x)
Therefore, the function is odd.

thank you very much