Question

HELP PLEASE< AM I RIGHT HERE? :

Answer 1

i think that I don't know what to do last, i know the first steps but not the lasts

Answer 2

i think it is even but again not sure

Answer 3

@volleyballlover55 @Sadlalkdja12111312 @mathmate

Answer 4

@Nnesha

Answer 5

I know I am supposed to replace x with -x and then see if the function stays the same or not, and with this one I got this ar: f(-x)=-x + 12/-x

Answer 6

So do you conclude that f(-x) does not equal f(x) or do you think they are equal?

Answer 7

thats the part I am not sure about because couldn't -x cancel the other -x out

Answer 8

in the other side of the function? and then it would be back to how it was originally

Answer 9

no, the -x in f(-x) cannot be cancelled with the -x on the right hand side.
The way to look at is is the following, if you're not sure.
f(x)=x+1/x
f(-x)=-x-1/x
If they are equal, when you subtract one from the other, you should get a zero, right?

Answer 10

yes

Answer 11

So let's do
f(x)-f(-x)
=x+1/x - (-x -1/x)
=?
can you work that out, taking care about the sign, and remember to distribute.

Answer 12

x+1/x^2 im sorr that was really confusing and I'm not sure i did it right

Answer 13

in the end though i worked it out and i think it will be even

Answer 14

if we continue the calculation, we have
x+1/x - (-x) - (-1/x)
=x+1/x+x+1/x
=2x+2/x
which is not a zero.
Since we say that f(-x) does not equal f(-x), what can you conclude?

Answer 15

that it is in fact an odd function. @mathmate

Answer 16

since they don't equal....

Answer 17

Unfortunately, there are functions that are neither odd nor even.
So you have to check if it is an odd function before you can say that.
As you know, an odd function will satisfy
f(x)=-f(-x).
Since you said f(-x)=-x-1/x
Can you tell me if f(-x) is the same as -f(x)?

Answer 18

no it isn't so it IS neither.. sorry

Answer 19

i forgot it could be neither, thats why i was confused

Answer 20

Not really, see we can factor out the negative sign.
-x-1/x = -(x+1/x)
which is the negative of f(x), so therefore f(-x)=-f(x).
What kind of function would that be?

Answer 21

even

Answer 22

since they are the same

Answer 23

Even: f(-x)=f(x)
Odd: f(-x)=-f(x).
Try again!

Answer 24

odd!

Answer 25

Yes, because we showed that
f(-x) = -x -1/x = -(x+1/x) = -f(x), so it is odd.

Answer 26

i said that first and i think you said it was wrong. Anyways, thank you so much! I understand.

Answer 27

If I missed it, I'm sorry about it.
You're welcome! :)