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a) Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.
b) The function is equivalent to the function
.
<h3>How to determine whether a limit exists or not</h3>
According to theory of limits, a function f(x) exists for x = a if and only if . This criterion is commonly used to prove continuity of functions.
<em>Rational</em> functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following <em>lateral</em> limits:
Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.
In addition, we can simplify the function by <em>algebra</em> properties:
The function is equivalent to the function
.
To learn more on lateral limits: brainly.com/question/21783151
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