Question 1205544
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You haven't posted a function, but I'll provide an example of domain in set-builder notation.


The function {{{f(x) = 1/(x-2)}}} has the domain *[tex \Large \big\{\text{x} | \text{x}\in\mathbb{R} , \  \text{x} \not = 2 \big\}] since x = 2 leads to a division by zero error. Any other x value will work.


The notation shown above translates to "The domain is x such that x is a real number and {{{x <> 2}}}"


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Another example:


{{{f(x) = sqrt(x-5)}}} has the domain *[tex \Large \big\{\text{x} | \text{x}\in\mathbb{R} , \  \text{x} \ge 5 \big\}]
If x = 5 or larger, then the stuff under the square root (aka radicand) is nonnegative.
If x < 5, then the radicand is negative, leading to f(x) outputs to be nonreal complex values.
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