QuestionFind the function and its domain, given , , .
Studdy Solution
STEP 1
Assumptions1. The function
. The function (although we don't use this in our problem)
3. The function
4. We are asked to find the function and its domain in interval notation
STEP 2
First, let's find the function by substituting and .
STEP 3
Substitute the given functions and .
STEP 4
Now, let's find the domain of . The domain of a function is the set of all possible input values (x-values) which will produce a valid output.
For the function , the denominator cannot be zero and it must be a real number. Therefore, must be greater than zero and must be less than4.
STEP 5
olving the inequality for gives
STEP 6
So, the domain of in interval notation is .
The function is and its domain is .
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