QuestionCalculate the product of and , and state its domain in interval notation.
Studdy Solution
STEP 1
Assumptions1. The functions are and .
. We need to find the product of these functions.
3. We also need to find the domain of the resulting function in interval notation.
STEP 2
First, we need to find the product of the functions and . This can be done by multiplying the two functions together.
STEP 3
Now, plug in the given functions for and to find the product.
STEP 4
Next, we simplify the product. We can do this by multiplying the numerators together and the denominators together.
STEP 5
Notice that the denominator is the negative of , so we can rewrite the product as
STEP 6
Now, we can cancel out the terms in the numerator and the denominator.
STEP 7
implify the product.
STEP 8
Next, we need to find the domain of the resulting function. The domain is all the real values of that make the function defined. The function is undefined where the denominator equals zero.
So, we set the denominator equal to zero and solve for .
STEP 9
olve the above equation for .
STEP 10
The function is undefined at . Therefore, the domain of the function in interval notation is .
The product of the functions and is and the domain of the resulting function in interval notation is .
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