Question

x+1=X-3has the value x=3 excluded from the(5 pts) If we know a rational function: f(x):domain, describe in words, what is the actual domain of the function? (Hint: It may helpyou to refer to the definition of domain and the idea that excluded means not included)Bonus: (+2 pts) Write that domain in interval notation. Use the symbol U to join yourtwo intervals together.

Answer 1

Given: The rational fraction below

$f(x)=\frac{x+1}{x-3},for,x\ne3$

To Determine: The domain of the function

Solution

$\begin{gathered} The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values \\ \:for\:which\:the\:function\:is\:real\:and\:defined \end{gathered}$

The function is undefined when x is equal to 3.

Hence, the domain of the function would be x less than 3 and x greater than 3.

Let us represents the domain in interval notation

$\begin{gathered} Domain:x<3,x>3 \\ Interval-notation \\ (-\infty,3)\cup(3,\infty) \end{gathered}$

Hence, the domain is (-∞,3) U (3, ∞)