How do you determine if #f(x)=1/x^2# is an even or odd function?
By substituting (1x) for all
Even function: NO sign changes Odd function: ALL signs change Neither: some signs change, some signs do not change.
Quick Trick for advanced students: Even functions: Every #x#term will have an even exponent, and a constant term may or may not exist. (#f(x)=x^4x^2+2# is an even function.
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To determine if ( f(x) = \frac{1}{x^2} ) is an even or odd function, we can use the following criteria:

Even function: If ( f(x) = f(x) ) for all ( x ) in the domain of ( f(x) ), then ( f(x) ) is an even function.

Odd function: If ( f(x) = f(x) ) for all ( x ) in the domain of ( f(x) ), then ( f(x) ) is an odd function.
For ( f(x) = \frac{1}{x^2} ), we have:
( f(x) = \frac{1}{(x)^2} = \frac{1}{x^2} = f(x) )
Since ( f(x) = f(x) ) for all ( x ) in the domain of ( f(x) ), ( f(x) ) is an even function.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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