How do you find the domain and range of #f(x)= x^2/(1x^2)#?
The domain is
The range is
Consequently,
We create a sign chart.
Therefore,
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To find the domain and range of ( f(x) = \frac{x^2}{1  x^2} ):

Domain: Identify values of ( x ) that make the function undefined. In this case, the function is undefined when the denominator, ( 1  x^2 ), equals zero. Thus, ( 1  x^2 \neq 0 ). Solving ( 1  x^2 = 0 ), we get ( x = \pm 1 ). So, the domain of ( f(x) ) is all real numbers except ( x = \pm 1 ).

Range: To find the range, observe the behavior of the function as ( x ) approaches positive and negative infinity. As ( x ) approaches positive or negative infinity, ( f(x) ) approaches positive infinity. Also, the function is symmetric about the yaxis. Hence, the range of ( f(x) ) is all real numbers greater than or equal to zero, excluding 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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