How do you determine if $F(x) = x^2-1$ is an even or odd function?

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Answer 1 · 2016-05-14T09:18:53

Observe that $F(-x) = F(x)$ and conclude that $F(x)$ is even.

A function $f(x)$ is even if $f(-x) = f(x)$ and is odd if $f(-x) = -f(x)$ . Thus, to check, we look at $F(-x)$ .

$F(-x) = (-x)^2-1=x^2-1=F(x)$

Thus, as $F(-x)=F(x)$ , we have that $F(x)$ is even.

How do you determine if F(x) = x^2-1F(x) = x^2-1 is an even or odd function?