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How do you determine if #g(x) = -6x + 5x^3# is an even or odd function?

Answer 1

Sadie Ackerman

Hence

#g(-x)=-6*(-x)+5*(-x)^3=6x-5x^3=-(6x+5x^3)=-g(x)#

Finally the function is odd because #g(-x)=-g(x)#

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Answer 2

Madelyn Anderson

To determine if the function ( g(x) = -6x + 5x^3 ) is even or odd, you evaluate ( g(-x) ) and compare it to ( g(x) ).

For an even function, ( g(x) = g(-x) ) for all ( x ) in the domain.

For an odd function, ( g(-x) = -g(x) ) for all ( x ) in the domain.

[ g(-x) = -6(-x) + 5(-x)^3 ] [ g(-x) = 6x - 5x^3 ]

Comparing ( g(-x) ) with ( g(x) ):

[ g(-x) \neq g(x) ]

[ g(-x) \neq -g(x) ]

Since neither condition holds, the function ( g(x) = -6x + 5x^3 ) is neither even nor odd.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.