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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

$g(-x)=(-x)_{4}+3(-x)_{2}−2$

Simplify right-hand side

$g(-x)=x_{4}+3x_{2}−2$

$g(x)$ | $g(-x)$ | $-g(x)$ |
---|---|---|

$x_{4}+3x_{2}−2$ | $x_{4}+3x_{2}−2$ | $-x_{4}−3x_{2}+2$ |

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