How do you determine if #g(x)= -9x^3 - 8# is an even or odd function?

Answer 1

#g(x)=-9x^3-8# is neither odd nor even.

If a function #g(x)# is even than #g(-x)=g(x)#
and if it is odd than #g(-x)=-g(x)#.
As #g(x)=-9x^3-8#,
#g(-x)=-9(-x)^3-8#
= #-9×(-x^3)-8#
= #9x^3-8# and hence
#g(-x)# is neither equal to #xgx)# nor equal to #-g(x)#.
Hence, #g(x)# is neither odd nor even.
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Answer 2

To determine if the function ( g(x) = -9x^3 - 8 ) is even or odd, follow these steps:

  1. Even Function: A function ( f(x) ) is even if ( f(-x) = f(x) ) for all ( x ) in the domain.

  2. Odd Function: A function ( f(x) ) is odd if ( f(-x) = -f(x) ) for all ( x ) in the domain.

For ( g(x) = -9x^3 - 8 ):

  • Substitute ( -x ) into the function: ( g(-x) = -9(-x)^3 - 8 ).

  • Simplify ( g(-x) ): ( g(-x) = -9(-x)^3 - 8 = -9(-x^3) - 8 = -9(-x^3) - 8 ).

Now, compare ( g(-x) ) with ( g(x) ):

  • If ( g(-x) = g(x) ), then the function is even.

  • If ( g(-x) = -g(x) ), then the function is odd.

For ( g(x) = -9x^3 - 8 ), ( g(-x) ) does not equal ( g(x) ) and ( g(-x) ) does not equal (-g(x)), so ( g(x) ) 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.

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.

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.

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.

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