Question

Determine whether -x^3/3x^2+5 is even, odd, or neither

Answer 1

If you can show that f(-x) = f(x), then the function f(x) is even


If you can show that f(-x) = -f(x), then the function f(x) is odd

Answer 2

But I don't know how to solve.

Answer 3

f(x) = (-x^3)/(3x^2+5)

f(-x) = (-(-x)^3)/(3(-x)^2+5)

f(-x) = (x^3)/(3x^2+5)


Since f(-x) is NOT equal to f(x), we know that f(x) is NOT even

Answer 4

It's odd?

Answer 5

yep because

f(x) = (-x^3)/(3x^2+5)

-f(x) = -(-x^3)/(3x^2+5)

-f(x) = (x^3)/(3x^2+5)

which is equal to f(-x)

Answer 6

Where did you get x^3?

Answer 7

its in the original problem

Answer 8

Sorry I was looking at something else/

Answer 9

Can you explain your steps please?

Answer 10

where are you stuck

Answer 11

I don't understand any of it.

Answer 12

going from

f(x) = (-x^3)/(3x^2+5)

to

f(-x) = (-(-x)^3)/(3(-x)^2+5)

I replaced each 'x' with '-x', then simplified to get

f(-x) = (x^3)/(3x^2+5)

Answer 13

Okay I get it now. Thank you... and one other thing.

Answer 14

How can I determine whether the equation y^2=6-x^2 defines y as a function of x

Answer 15

solve for y, if you get one single equation for y, then the equation is a function

if you get more than one equation, then the equation is not a function

Answer 16

Solving for Y will I replace x with 0?

Answer 17

no just isolate y

Answer 18

in terms of x

Answer 19

you want y = ...

Answer 20

Right so at the moment it is y^2=6-x^2

Answer 21

yep, then what

Answer 22

I need to get rid of the square by using a square root?

Answer 23

yep, that's correct, so what do you get when you do that