SOLUTION: Explain how to use -x to determine if a. f(x) is an even function. b. f(x) is an odd function. c. Use your explanation to show f(x)= x^3 - 8x is an even function, an odd

Algebra ->  Rational-functions -> SOLUTION: Explain how to use -x to determine if a. f(x) is an even function. b. f(x) is an odd function. c. Use your explanation to show f(x)= x^3 - 8x is an even function, an odd       Log On


   

Question 1200530: Explain how to use -x to determine if
a. f(x) is an even function.
b. f(x) is an odd function.
c. Use your explanation to show f(x)= x^3 - 8x is an even function, an odd function, or neither.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
here's a reference.
https://www.mathsisfun.com/algebra/functions-odd-even.html


your example is f(x) = x^3 - 8x.

it will be even if f(x) = f(-x) for all values of x.
you get:
f(x) = x^3 - 8x
f(-x) = (-x)^3 - 8(-x) = -x^3 + 8x
since f(x) does not equal f(-x), then it is not an even function.

it will be odd if -f(x)= f(-x)
-f(x) = -(x^3 - 8x) = -x^3 + 8x
f(-x) = (-x)^3 - 8(-x) = -x^3 + 8x
since -f(x) = f(-x), then it is an odd function.
for example, let x = 2.
-f(2) = -(2^3 - 8*2) = -(8-16) = -(-8) = 8
f(-x) = (-2)^3 - 8*-2) = -8 -(-16) = -8 + 16 = 8.

check out the reference.
it explains it pretty well.