Question

Find the domain of the following expressions:

Answer 1

Part 1) The domain is the interval (-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) The domain is the interval (-∞,0) ∪ (0,2) (2,∞)

Part 3) The domain is the interval (-∞,-6) ∪ (-6,6) ∪ (6,∞)

Explanation:

Part 1) we have

`(32)/(y)-(y+1)/(y+7)`

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 0 or cannot be equal to -7

The domain for y is all real numbers except the number -7 and the number 0

The domain in interval notation is

(-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) we have

`(y^2+1)/(y^2-2y)`

we know that

The denominator cannot be equal to zero

`y^2-2y=0\\y^2=2y\\y=2`

so

The value of y cannot be equal to 0 or 2

The domain for y is all real numbers except the number 0 and 2

The domain in interval notation is

(-∞,0) ∪ (0,2) (2,∞)

Part 3) we have

`(y)/(y-6)+(15)/(y+6)`

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 6 or cannot be equal to -6

The domain for y is all real numbers except the number -6 and the number 6

The domain in interval notation is

(-∞,-6) ∪ (-6,6) ∪ (6,∞)