How do you determine if $f(x) = 5x^-2 - 4x^4$ is an even or odd function?

Question

1782 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-18T10:31:41

$color(blue)("Even")$

A function is even if:

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

A function is odd if:

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

Test for even:

$f(x)=5x^(-2)-4x^4=5/(x^2)-4x^4$

$f(-x)=5(-x)^(-2)-4(-x)^4=5/((-x)^2)-4(-x)^4=5/x^2-4x^4$

$:.$

$f(x)=f(-x)$ the function is even.

How do you determine if f(x) = 5x^-2 - 4x^4f(x) = 5x^-2 - 4x^4 is an even or odd function?