Is the function odd, even or neither?

Question

f(x)=x^2/x-1

This is what I have done, I could be wrong.
f(-x) = (-x)^2/(-x)-1
= x^2/-x-1
= x^2/-(x-1)
= -x^2/x-1
Therefore, it is odd
Did I do this right?

Answer 1

I'm not quite sure what you have proved, but if you look at your second to third step, you factor out a negative sign without changing the -x-1 to -(x+1). Instead, you leave it as is: -(x-1) which is wrong.

Answer 2

By defininition

if x is a real valued function then f(x) iis defined to be real

and if F(x)=F(-x) is even.

examples of even functions are x^2,cos(x)..etc

and if -F(x)=F(-x) the definition states the function is odd.

examples of odd functions are x^3 and sin(x)..

if for example the function is a sum of even and odd the
function would be neither

examples might be
x^3+x^2.




for F(x)=x^2/(x-1).......of -x to see if
this equals
-f(x) for odd or f(x) for even.



-x^2/(-x-1)=x^2/(-x-1)= -x^2/(x+1)

So a -f(x)= -x^2/(x-1) for odd
and
f(x)=x^2/(x-1) for even

in this case you have
f(x)= -x^2/(x+1)

so the function is neither

Answer 3

you have to simplify it first
so x^2-1/x-1=
(x-1)(x+1)/(x-1)
=x+1
to indicate the function is odd or even or neither
f(-x)=-x+1
take (-ve) a common factor=
-(x-1)
therefore the function is neither even nor odd

Answer 4

-x-1 is not -(x-1= which is -x+1 The function is not even nor odd

Answer 5

No. Actually -x - 1 = -(x + 1). It is neither.

Answer 6

odd function definition f(x)= -f(-x)

f(-x) = (-x)^2/(-x)-1
= x^2/-x-1
= x^2/-(x+1) *ERROR in your calculation here*
= -x^2/x+1

f(x) not equal -f(-x)
so the answer is neither

Answer 7

neither