what is the domain in interval notation when the restrictions are x cannot = 2 and x cannot = -2?
I got (-infinity, 2) U (2,-infinity)
(-infinity, -2) U (-2, infinity)
but my math teacher marked this as wrong
think about it. You want
(-∞,-2)U(-2,2)(2,∞)
You have duplicated some intervals and overlapped them.
forgot the 2nd U. Should be
(-∞,-2)U(-2,2)U(2,∞)
To determine the domain in interval notation with the given restrictions, you need to exclude the values of x that are not allowed.
In this case, x cannot equal 2 and x cannot equal -2.
To represent this in interval notation, you should write it as (-infinity, -2) U (-2, 2) U (2, infinity).
So the correct answer is (-infinity, -2) U (-2, 2) U (2, infinity).
To determine the domain in interval notation when the restrictions are x cannot equal 2 and x cannot equal -2, we need to consider two separate intervals.
First, let's consider the interval when x cannot equal 2. This means that x can take any value except 2. We can represent this interval as (-∞, 2) U (2, ∞), where U denotes the union of the two intervals.
Now, let's consider the interval when x cannot equal -2. This means that x can take any value except -2. We can represent this interval as (-∞, -2) U (-2, ∞).
However, we need to find the common values between these two intervals, which represent the values that cannot be taken by x. In this case, the value that cannot be taken by x is 2, so we need to exclude it from both intervals.
The correct representation of the domain in interval notation is then (-∞, -2) U (-2, 2) U (2, ∞). This notation indicates that x can take any value except -2 and 2. It's possible that your math teacher marked your answer wrong because you inadvertently included -2 and 2 as part of the domain, which is not allowed according to the given restrictions.