Find the domain of each function using interval notation. ( i have an exam tomorrow and i’m really stuck)

For number 9)

Interval notation

For number 10)

Interval notation: .

Step-by-step explanation:

On square roots you have to make sure the inside is positive or zero.

So the domain of the first one will come from solving

Subtract 6 on both sides:

Divide both sides by -2 (flip inequality when divide both sides by negative):

The domain is less than or equal to 3.

Interval notation

On fractions you have to watch out for dividing by 0.

The domain is all real numbers except when 4x+2=0.

4x+2=0

Subtract 2 on both sides:

4x=-2

Divide both sides by 4:

x=-2/4

Reduce:

x=-1/2

The domain is all real numbers except when x=-1/2

Interval notation: .

9.

15.

Step-by-step explanation:

9.

The function has a square root. Since you cannot take the square root of a negative number, the expression in the root must be non-negative.

15.

There is a denominator int he function. The denominator cannot equal zero. Set the denominator equal to zero to find out the value that must be excluded from x.