Question

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

f(x) = -9 x^3 + 8x

Answer 1

help!

Answer 2

for an even function

substitute -x and you should get the orginal function

e.g. f(x) = x^2 + 5 f(-x) = (-x)^2 + 5 = x^2 + 5

so its even

for odd functions ... f(-x) = - f(x)

since your function has a highest power of 3 it may be odd

so substitute x = -x and check

f(-x) = -9(-x)^3 + 8(-x)

when you simplify it, will you get the negative version of the original function..?

Answer 3

a function that is neither odd nor even... won't be f(x) or -f(x) when x = -x is substituted.

e.g.

f(x) = x^2 + 2x f(-x) = (-x)^2 + 2(-x) = x^2 - 2x which is neither odd nor even.

hope this helps

Answer 4

@campbell_st oh so it's neither?

Answer 5

so looking at the problem

f(-x) = -9(-x)^3 + 8(-x)
= -9(-x^3) - 8x
= 9x^3 - 8x

= -(-9x^3 + 8x)

so

f(-x) = - f(x)

so the function is odd.

Answer 6

thanku!!!:)