Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Three More Even, Odd or Neither Functions

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

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Three More Even, Odd or Neither Functions

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Three More Even, Odd or Neither Functions

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

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Three More Even, Odd or Neither Functions

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Three More Even, Odd or Neither Functions

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.