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How do you determine if #f(x)= X^11 + X^9# is an even or odd function?

Answer 1

Madelyn Anderson

#f(x)=x^11+x^9# is an odd function.

If #f(-x)=f(x)#, #f(x)# is an even function. And if #f(-x)=-f(x)#, #f(x)# is an odd function.

Here we have #f(-x)=x^11+x^9# and hence

#f(-x)=(-x)^11+(-x)^9=-x^11-x^9=-(x^11+x^9)=-f(x)#

As such, #f(-x)=x^11+x^9# is an odd function.

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Answer 2

Sophie Adams

To determine if the function ( f(x) = x^{11} + x^9 ) is even or odd:

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

Let's check both conditions for ( f(x) = x^{11} + x^9 ):

Even function: ( f(x) = x^{11} + x^9 ) ( f(-x) = (-x)^{11} + (-x)^9 = x^{11} - x^9 ) Since ( f(x) = x^{11} + x^9 ) is not equal to ( f(-x) = x^{11} - x^9 ) for all ( x ), the function is not even.
Odd function: ( f(x) = x^{11} + x^9 ) ( -f(-x) = -(-x)^{11} - (-x)^9 = -x^{11} + x^9 ) Since ( f(x) ) is not equal to ( -f(-x) ) for all ( x ), the function is not odd.

Therefore, the function ( f(x) = x^{11} + x^9 ) 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.