# Thread: function is even, odd, or neither?

1. ## function is even, odd, or neither?

How would I go about doing that?

Let's say f(x) = 17x^322 for example....

2. Hello,
Originally Posted by realintegerz
How would I go about doing that?

Let's say f(x) = 17x^322 for example....
To say so, find $f(-x)$

Here, $f(-x)=17*(-x)^{322}=17*((-1)*x)^{322}$

Using this rule : $(ab)^c=a^c b^c$, we get

$f(-x)=17*x^{322}*(-1)^{322}=f(x)*(-1)^{322}$

Using the rule of exponents : $a^{bc}=(a^b)^c$, we can say that $(-1)^{322}=[(-1)^2]^{161}=1^{161}=1$

Thus $f(-x)=f(x)$

Got it ?

3. so if f(-x) = f(x) it is even, and if it doesnt it is odd?

how do i know when its neither...

4. Originally Posted by realintegerz
so if f(-x) = f(x) it is even, and if it doesnt it is odd?

how do i know when its neither...
NO!

Even: f(-x) = f(x).

Odd: f(-x) = - f(x).

Otherwise neither even nor odd.