How do you find the domain and range of #f(x) = 2 / (1  x²)#?
Domain is defined by inequalities:
Range is a combination of two intervals
graph{(1x^2) [5, 5, 10, 10, 5]}
graph{1/(1x^2) [10, 10, 5, 5, 10]}
graph{2/(1x^2) [10, 10, 5, 5, 10]}
Because of this, the range is shown as two intervals:
or, using a different symbol,
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To find the domain and range of ( f(x) = \frac{2}{1  x^2} ):

Domain: The function is defined for all real numbers except where the denominator becomes zero, which would result in division by zero. So, the domain is all real numbers except where ( 1  x^2 = 0 ).
( 1  x^2 = 0 ) when ( x^2 = 1 ).
So, ( x = \pm 1 ).
The domain of the function is all real numbers except ( x = \pm 1 ).

Range: To find the range, consider the behavior of the function as ( x ) approaches positive and negative infinity. As ( x ) approaches positive or negative infinity, ( 1  x^2 ) approaches positive infinity.
Therefore, as ( x ) approaches positive or negative infinity, ( f(x) = \frac{2}{1  x^2} ) approaches zero.
The range of the function is all real numbers except zero.
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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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