Is f odd, even, or neither?

Question

Let f(x) = (3x²-9)/(x²-1)
(a) What is the domain of f?
(b) Is f odd, even, or neither?

Answer 1

Hi Pius,

 

First of all, thank you for using parentheses and making life easy for everyone!

 

a) The domain will exclude the values of that make the denominator zero. So, x^2-1 = 0 and we get x={-1, 1}

The domain of f(x) is all real numbers except -1 and 1.

 

b) The definition of even and odd function is as follows:

if f(-x) = f(x) then the function is even

if f(-x) = -f(x) then the function is odd

In all other cases, the function is neither even nor odd.

 

So, let's check.

f(x) = (3x^2-9)/(x^2-1)

plug in -x for x

=(3(-x)^2 -9) / ((-x)^2-1)

= (3x^2 - 9) / (x^2 - 1)

we see that f(x) = f(-x) and conclude that it is an even function.