Question

is f(x)=x^4-5x^2+4 an odd function and if so why?

Answer 1

An odd function in an exponential would be if the exponent is odd

Answer 2

It also depends on the symmetry

Answer 3

-f(x) = -x^4+5x^2-4
f(-x) = (-x)^4-5(-x)^2+4 = x^4-5x+4 = f(x)
thus it is even

Answer 4

this function is in fact even
it is a polynomial with all even exponents

Answer 5

that should say f(-x) = (-x)^4-5(-x)^2+4 = x^4-5x^2+4 = f(x)

Answer 6

thank you!

Answer 7

You could also inspect \(x^4\) which is a parabola that kind of looks like an M, and graphing it you could see it's an even function where \[\large \color{#ff2255}{f(-x)}=\color{#ff3322}{f(x)}\]

Answer 8

To prove that it is an even function instead of an odd, plug in negative values of x, and simplifying your function you should get an positive outcome. If you plug in negative numbers and end up with a negative outcome it's odd.

Answer 9

note with functions, things can be neither even nor odd

Answer 10

Ohh... plugging in an a negative eor positive number would both result in 0, this can be NENO or neither even nor ODD. Ahh....

Answer 11

if f(-x) = f(x) it is even
if f(-x) = -f(x) it is odd
note: x^2 = (-x)^2