QuestionIdentify the restrictions on the domain of
Studdy Solution
STEP 1
What is this asking?
We need to find which values of would cause trouble for the function , specifically making the denominator zero.
Watch out!
Don't mix up the numerator and denominator; we only care about the denominator here!
Also, be careful with the signs.
STEP 2
1. Examine the Denominator
2. Find the Restricted Value
3. State the Domain
STEP 3
Alright, so we've got this cool function, , and we're on the lookout for any **domain restrictions**.
What could possibly go wrong with this function?
Well, the only thing that could cause a problem is if we divide by **zero**.
STEP 4
Remember, dividing by zero is a big no-no in math!
It's like trying to divide a pizza into zero slices – it just doesn't make sense!
So, we need to make sure that the denominator of our function, , is **never equal to zero**.
STEP 5
Let's set up an equation to find the value of that would make the denominator zero:
STEP 6
To solve for , we need to get by itself.
We can do this by adding to **both sides** of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!
STEP 7
So, we found that when , the denominator becomes .
This is exactly what we're trying to avoid!
STEP 8
The **domain** of a function is all the possible values that can take.
Since we found that can be any value *except* , we can write the domain as .
This means can be any other number, big or small, positive or negative, but it just can't be .
STEP 9
The restriction on the domain of is .
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