Question

State the symmetryf(x) = x4 + 2x3 - 4x

Answer 1

Problem

$\text{State the symmetry of f(x) = x}^4+2x^3\text{ - 4x}$

Method

A symmetric function is a function in several variable which remain unchanged for any permutation of the variables.

f(-x) = f(x)

Final answer

$\begin{gathered} f(x)=x^4+2x^3\text{ - 4x} \\ \\ f(-x)\text{ = }x^4+2(-x)^3\text{ - 4(-x)} \\ f(-x)=x^4-2x^3\text{ + 4x} \end{gathered}$

from the final solution

$\begin{gathered} f(x)\text{ }\ne\text{ f(-x)} \\ \text{Hence, the function is not symmetric} \end{gathered}$