QuestionFind the domain of the functions: and .
Studdy Solution
STEP 1
Assumptions1. We are looking for the domain of the functions and .
. The domain of a function is the set of all possible input values (x-values) which will produce a valid output (y-value).
3. For the square root function, the expression inside the square root must be greater than or equal to zero.
4. For the reciprocal function, the denominator cannot be zero.
STEP 2
First, let's find the domain of the function .
The expression inside the square root must be greater than or equal to zero. So, we set up the inequality
STEP 3
Next, we solve the inequality for x.
To do this, we first subtract2 from both sides
STEP 4
Then, we multiply both sides by -1 to get x by itself. Remember that when we multiply or divide both sides of an inequality by a negative number, we must flip the direction of the inequality sign.
So, the domain of the function is all x such that .
STEP 5
Now, let's find the domain of the function .
The denominator cannot be zero, so we set up the equation
STEP 6
This equation simplifies toSo, the domain of the function is all x such that .
Was this helpful?