Odd & Even Functions... 10 points for a good answer?

Question

Is this an odd or even function? Explain please

f(x) =

x
-------------
(x^2 -1)

x^2 -1 is an even function

x is an odd function

and when you sub in f(-x), you cant turn it into an even or odd function, which is expected, as it is neither

However, when you graph the function, it turns out as an odd function, which came to a big surprise to me

I though that if we broke down x^2 -1 into (x-1)(x+1), and then try it, the -1's still cancel each other out, as if they'd been squared, and when you actually sub the values in for f(x), it does form an odd curve!

The equation is saying its neither and the graph is saying its odd! Punch it in a program and you'll see xD... ='(

I'm lost. Either I'm forgetting something or I didn't understand odd and even's when I did them a while back.

Can somebody explain this, because I aint gonna sleep till I get this.... lol xD - 2 am here

dwayne w, - please put the equation in a graphing program, it'll show you its an odd function.

Btw, if f(x) = x

f(-x) = -1(x), its an odd function

x^2 -1 is even

how did you prove it was even, I dont get how you used the binomial lol ='(, please show me

BOND- Thats what I said, however will you please just graph the equation....!

You will see it form an odd function

Read the question please guys!!! xD

OMFG I'M A COMPLETE IDIOT LOL

I GET IT NOW! Excuse me for 1 moment while I go back to year 7 algebra please

Thanks a bunch guys!

Answer 1

f( - x) =

- x / ( [- x] ^2 - 1) = - { x / ( x ^2 - 1) } = - f(x)

and so f(x) is ODD

Answer 2

the product of two odd functions will be an even function when you multiply exponents, you add x^3*x^5=x^(3+5)=x^8

Answer 3

An even function has the following property:
f(x)=f(-x)
For an odd function the property is:
f(x)=-f(-x) or -f(x)=f(-x)
Let's verify our functions:
for f(x)=x see how f(-x) looks like
f(-x)=-x=-f(x), which means that f(x)=x is an odd function
An odd function is symmetric relatively to the origin of the coordinate system and the f(x)=x graph is symmetric relatively to the origin.

for f(x)=x^2-1
f(-x)=(-x)^2-1=x^2-1=f(x)
Therefore, we obtained that f(-x)=f(x). We conclude that f is an even function in this case.
The graph of an even function is symmetric relatively to the Y-axis. f(x)=x^2-1 is symmetric relatively to the Y-axis. It is a quadratic with the minimum point on the Y axis (at x=0, y=1).

So, in general, verify f(-x) and see if it is equal to f(x), f(-x) or different altogether.

Answer 4

The definition of an even function is:

f(x) = f(-x) For example let f(x) = x^2, then f(-x) = (-x)^2 = x^2

An odd function is:

f(-x) =-f(x) for example f(x)=x^3 --> f(-x) = (-x)^3 =(-1)^3x^3 =-x^3 =-f(x)

Now your funciton is:

f(x) = x/(x^2-1) let x -> -x then

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

So this is an odd function. You don't need the binomial expansion.

Answer 5

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

So f(x) is odd function.

For ascertaining whether a function is even or odd just check
if f(-x) = f(x); f(x) is even
if f(-x) = -f(x); f(x) is odd

Answer 6

f(x)=x/(x^2-1)
f(-x)= -x / ((-x)^2-1) = -x/ (x^2-1)
Since f(x) is not equal to f(-x), this is not an even function.

-f(x) = -x/(x^2-1) = f(-x) as we proved above.
So this is an odd function.

Answer 7

See if x is odd
x+1 and x-1 are even therefore x^2 - 1 is even
Now odd/even
is of form m/2n
because odd no. does not have 2 as a factor.
m/2n comes out to be 0.5 m/n
even if n is 1 still m/2n is a fraction or a decimal which is why
it cannot be an integer so it is neither even nor odd.

Answer 8

It is an even function as when you break it down as find the binomial distribution it is an even function it is hard to expalin but I worked out the problem