Evaluate. f ( x ) = x 3 − 4 x

Question

Evaluate.   f  (  x  )  =      x          3            ﻿    −  4  x

nezivande0u · Accepted Answer

A function is said to be even if and only if
f(x)=f(-x)
a function is said to be odd if and only if
-f(x)=f(-x)
sp we got:

f (x) = x^{3} - 4 x

lets work on f(-x) because is unavoidable
if a function is even, it can't be odd

f (- x) = (- x)^{3} - 4 (- x) = - x^{3} + 4 x

now lets work on the even function
f(x)=f(-x)

x^{3} - 4 x = - x^{3} + 4

false, so this os not even function
checking for odd-function:

- f (x) = - (x^{3} - 4 x) = - x^{3} + 4 x

- x^{3} + 4 x = - x^{3} + 4 x

Greyson Landry · Accepted Answer

For this equation,
Evenmeans, that the graphed line is symmetric to the y-axis. Odd meansthat the graphed line is symmetric to the y-axis. To figure if afunction is even or odd, you change the variables. For thisequation, the line is, an odd function. This is because, if youchange the x's to -x's (even function) it is not the same equation.If, you change the x's to -x's and the y's to -y's (odd function)it is the same equation. Example: (even)

f (x) = x^{3} - 4 x \neq f (x) = - (x^{3}) - (- 4 x)

(odd)

f (x) = x^{3} - 4 x = f (- x) = - (x^{3}) - (- 4 x)

Evaluate. f(x) = x^3-4x

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