Three More Even, Odd or Neither Functions

mathxyz · 2024-03-20 17:29:35

Determine if each function is even, odd, or neither.

1. f(x) = cuberoot{2x^2 + 1}

f(-x) = cuberoot{2(-x)^2 + 1}

f(-x) = cuberoot{2x^2 + 1}

I say even.

2. h(x) = x/(x^2 - 1)

h(-x) = -x/((-x)^2 - 1)

h(-x) = -x/(x^2 - 1)

I say odd.

3. F(x) = 2x/|x|

F(-x) = 2(-x)/|-x|

F(-x) = -2x/x

F(-x) = -2

Neither even or odd.

You say?

Bob · 2024-03-20 20:48:00

1 and 2 are correct.

Think again about 3. If x is positive 2x/|x| = 2x/x = 2 If x is negative 2x/|x| = 2x/-x = -2

Bob

mathxyz · 2024-03-21 02:37:13

Bob wrote:

1 and 2 are correct.
Think again about 3. If x is positive 2x/|x| = 2x/x = 2 If x is negative 2x/|x| = 2x/-x = -2
Bob

Understood but this further agrees that the answer is neither.

Bob · 2024-03-21 03:49:03

Definition:

A function is "odd" when:

−f(x) = f(−x) for all x

In this question f(x) = 2 f(-x) = -2 = -f(x) This is an odd function.

Bob

mathxyz · 2024-03-21 09:07:16

Bob wrote:

Definition:
A function is "odd" when:
−f(x) = f(−x) for all x
In this question f(x) = 2 f(-x) = -2 = -f(x) This is an odd function.
Bob

Thank you very much.

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