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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

$f(-x)=(-x)_{5}+3(-x)_{4}$

NegBaseToNegPow$(-a)_{5}=-a_{5}$

$f(-x)=-x_{5}+3(-x)_{4}$

NegBaseToPosPow$(-a)_{4}=a_{4}$

$f(-x)=-x_{5}+3x_{4}$

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

$x_{5}+3x_{4}$ | $-x_{5}+3x_{4}$ | $-x_{5}−3x_{4}$ |

Since $f(x) =f(-x)$ and $f(-x) =-f(x),$ the function $f$ is neither an even nor an odd function.