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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Before we begin, let's recall two important definitions.

- A function $f$ has even symmetry when $f(-x)=f(x)$ for all $x$ in its domain.
- A function $f$ has odd symmetry when $f(-x)=-f(x)$ for all $x$ in its domain.

Reset

$f(-x)=-2(-x)_{6}+(-x)_{2}$

Simplify right-hand side

$f(-x)=-2x_{6}+x_{2}$

$f(x)$ | $f(-x)$ | $-f(x)$ |
---|---|---|

$-2x_{6}+x_{2}$ | $-2x_{6}+x_{2}$ | $2x_{6}−x_{2}$ |

We can see above that $f(x)=f(-x).$ Therefore, $f$ has even symmetry.