QuestionFind , , , and for given functions and in three cases.
Studdy Solution
STEP 1
Assumptions1. We are given two functions, and .
. We are asked to find the addition, subtraction, multiplication, and division of these functions.
3. The operations on the functions are performed element-wise, i.e., the operations are performed on the corresponding elements of the functions.
STEP 2
For the first pair of functions, and , we are asked to find .
The addition of two functions is defined as
STEP 3
Substitute the given functions into the formula
STEP 4
implify the expression
STEP 5
Next, we are asked to find .
The subtraction of two functions is defined as
STEP 6
Substitute the given functions into the formula
STEP 7
implify the expression
STEP 8
Next, we are asked to find .
The multiplication of two functions is defined as
STEP 9
Substitute the given functions into the formula
STEP 10
Expand the expression
STEP 11
implify the expression
STEP 12
Finally, we are asked to find .
The division of two functions is defined as
STEP 13
Substitute the given functions into the formula
STEP 14
This expression cannot be simplified further, so we leave it as is.
So, for the first pair of functions, we have
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