Question

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

Answer 1

`f(x)` is neither odd nor even.

Explanation:

If a function `f(x)` is even than `f(-x)=f(x)` and if it is odd than `f(-x)=-f(x)`.

As `f(x)=(x-2)^2+1`,

`f(-x)=(-x-2)^2+1`

= `(x+2)^2+1` and hence

`f(-x)` is neither equal to `f(x)` nor equal to `-f(x)`.

Hence, `f(x)` is neither odd nor even.