help!! my homework is due in 4 hours and I have no clue what to do

Question

Give the domain of m ( x ) = √ − 11 − x in interval notation.

Answer 1

A sguare root can only be taken of something greater than or equal to 0.

To find the domain you must solve:

–11–x ≥ 0

add x to both sides:

–11 ≥ x

Therefore the domain must be x ≤ –11 or in interval notation (–∞, –11)

Hope this helps!

Answer 2

The domain is asking for all possible inputs or x values for this function. Essentially, if you were to graph it, which x values are covered by the line.

I am assuming the function is m(x) = sqrt(-11-x). Since a square root of a negative number is imaginary, we need to find all cases where (-11-x) is positive. In other words, when (-11 - x) is greater than or equal to 0. We can set up this inequality below.

-11 - x >= 0 (I am using >= to represent > with a line underneath it)

(let's add x to both sides)

-11 >= x

This tells us the domain is where x is less than or equal to -11, as represented below.

x <= -11. This represents the domain of the function m(x).