Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x)=x+12/x

Answer 1

to show that the function is even, you must show that f(x) = f(-x)
to show that the function is odd you must show that f(x) = - f(-x)

Answer 2

In order to determine algebraically whether the function is even or odd or neither, plug in -x for x and simplify it. It the result is the same then it is even, if the result is is the exact opposite of what you started with, by which I mean that the sign on each term has been changed to its opposite, just as if multiplied through by –1, then it is odd. If neither of them happens, then it is neither. Does this make sense?

Answer 3

kinda.. yeah.. so would for this id be odd right?

Answer 4

Is it odd? If I plug -x, the result should be -x - 12/x. Let's test it.

f(x) = x + 12/x
f(-x) = (-x) + 12/(-x) = -x - 12/x

Yes, it is odd.

Answer 5

ahh thankyou!!

Answer 6

Glad you got it.