Determine whether each function is even, odd, or neither.

1. [tex]f(x) = x^6 - x^2[/tex]

2. [tex]f(x) = 2x^3 - x[/tex]

f ( x ) = x 6 − x 2 f ( − x ) = ( − x ) 6 − ( − x ) 2 = x 6 − x 2 f ( − x ) = f ( x ) ⇒ even f ( x ) = 2 x 3 − x f ( − x ) = 2 ( − x ) 3 − ( − x ) = − 2 x 3 + x f ( − x )  = f ( x ) ⇒ not even − f ( x ) = − ( 2 x 3 − x ) = − 2 x 3 + x − f ( x ) = f ( − x ) ⇒ odd

Answered by konrad509 | 2024-06-10

The function f ( x ) = x 6 − x 2 is even because f ( − x ) = f ( x ) . The function f ( x ) = 2 x 3 − x is odd because f ( − x ) = − f ( x ) .
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Answered by konrad509 | 2024-12-26