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How do you determine if #F(x) = x^2-1# is an even or odd function?

Answer 1

Anna Allen

Observe that #F(-x) = F(x)# and conclude that #F(x)# is even.

A function #f(x)# is even if #f(-x) = f(x)# and is odd if #f(-x) = -f(x)#. Thus, to check, we look at #F(-x)#.

#F(-x) = (-x)^2-1=x^2-1=F(x)#

Thus, as #F(-x)=F(x)#, we have that #F(x)# is even.

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Answer 2

Caleb Alexander

To determine if ( F(x) = x^2 - 1 ) is an even or odd function, we evaluate ( F(-x) ) and compare it with ( F(x) ).

If ( F(-x) = F(x) ) for all ( x ) in the function's domain, then the function is even.

If ( F(-x) = -F(x) ) for all ( x ) in the function's domain, then the function is odd.

For ( F(x) = x^2 - 1 ):

Evaluate ( F(-x) ): ( F(-x) = (-x)^2 - 1 = x^2 - 1 )
Compare ( F(-x) ) with ( F(x) ): ( F(-x) = F(x) )

Since ( F(-x) = F(x) ) for all ( x ), the function ( F(x) = x^2 - 1 ) is an even function.

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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.