Sally found that a solution of x = 2 was extraneous for her function. What would be a possible denominator in Sally's function?
2 answers:
If you have a fraction, then the denominator (bottom) cannot equal 0, since it is impossible to divide by 0. Take a look at the function below.
If we plugged in 2 for x, we would end up with a denominator of 0, making x = 2 "extraneous."
(you can use this example to answer your question, with the denominator being x-2...any expression that evaluates to 0 when x = 2 would work)
If we plugged in 2 for x, we would end up with a denominator of 0, making x = 2 "extraneous."
(you can use this example to answer your question, with the denominator being x-2...any expression that evaluates to 0 when x = 2 would work)
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Answer:
see picture with work shown
<h2>Hello!</h2>
The answer is:
The domain of the function is all the real numbers except the number 13:
Domain: (-∞,13)∪(13,∞)
<h2>Why?</h2>This is a composite function problem. To solve it, we need to remember how to composite a function. Composing a function consists of evaluating a function into another function.
Composite function is equal to:
So, the given functions are:
Then, composing the functions, we have:
Therefore, we must remember that the domain are all those possible inputs where the function can exists, most of the functions can exists along the real numbers with no rectrictions, however, for this case, there is a restriction that must be applied to the resultant composite function.
If we evaluate "x" equal to 13, the denominator will tend to 0, and create an indetermination since there is no result in the real numbers for a real number divided by 0.
So, the domain of the function is all the real numbers except the number 13:
Domain: (-∞,13)∪(13,∞)
Have a nice day!