# How do you determine if #f(x)=1+3x^3-x^5# is an even or odd function?

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To determine if ( f(x) = 1 + 3x^3 - x^5 ) is an even or odd function, you evaluate ( f(-x) ) and compare it with ( f(x) ).

If ( f(-x) = f(x) ), the function is even. If ( f(-x) = -f(x) ), the function is odd.

For ( f(x) = 1 + 3x^3 - x^5 ),

( f(-x) = 1 + 3(-x)^3 - (-x)^5 )

( = 1 - 3x^3 - x^5 )

Since ( f(-x) \neq f(x) ) and ( f(-x) \neq -f(x) ), the function ( f(x) = 1 + 3x^3 - x^5 ) is neither even nor odd.

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