Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = 3x2 - 1

Answer 1

A function \(f(x)\) is even if \(f(-x)=f(x)\), and odd if \(f(-x)=-f(x)\). (Neither if neither condition is met.

So to show the given function is even or odd, you plug in \(-x\). You get
\[f(-x)=3(-x)^2-1=3x^2-1=f(x)\]
hence \(f(x)\) is even.

Answer 2

Thank you, one more question relating to this. Is this related to function inverses?