How do you determine if #f(x)=sqrt( x^2 3)# is an even or odd function?
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To determine if ( f(x) = \sqrt{x^2  3} ) is an even or odd function, follow these steps:

Even Function:
 A function ( f(x) ) is even if ( f(x) = f(x) ) for all ( x ) in its domain.
 Substitute ( x ) into the function and simplify. If the result is the same as the original function, ( f(x) ), then the function is even.

Odd Function:
 A function ( f(x) ) is odd if ( f(x) = f(x) ) for all ( x ) in its domain.
 Substitute ( x ) into the function, negate the result, and simplify. If the result is the same as the original function multiplied by 1, then the function is odd.
Let's apply these steps to ( f(x) = \sqrt{x^2  3} ):

Even Function Test: [ f(x) = \sqrt{(x)^2  3} = \sqrt{x^2  3} = f(x) ]
Since ( f(x) = f(x) ), the function passes the even function test.

Odd Function Test: [ f(x) = \sqrt{(x)^2  3} = \sqrt{x^2  3} ] [ f(x) = \sqrt{x^2  3} ]
Since ( f(x) ) is not equal to ( f(x) ), the function does not pass the odd function test.
Conclusion:
 ( f(x) = \sqrt{x^2  3} ) is an even function because ( f(x) = f(x) ) for all ( x ) in its domain.
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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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