Is the function even,odd, or neither

Question

asked Jan 20, 2022 124k views

2 Answers

James Berkenbile · Answer 1 · 2022-01-24T06:20:56+0000

Answer:

Neither

Explanation:

If f (–x) = f (x), then the function is even. if f (–x) = –f (x), (all the signs are flipped) the it is odd.

To apply this to the function here, simply replace the x in
(x-2)^(2) with -x.

(x-2)^(2) =
x^(2) - 4x + 4, and
(-x - 2)^(2) =
x^(2) +4x + 4.

Since
x^(2) +4x + 4 doesnt equal
x^(2) - 4x + 4 (even) or
-x^(2) +4x -4 (odd), the function is neither even nor odd.