Answer:
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,∞)
Step-by-step explanation:
Part 1) we have
[tex]\frac{32}{y}-\frac{y+1}{y+7}[/tex]
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
[tex]\frac{y^2+1}{y^2-2y}[/tex]
we know that
The denominator cannot be equal to zero
[tex]y^2-2y=0\\y^2=2y\\y=2[/tex]
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
[tex]\frac{y}{y-6}+\frac{15}{y+6}[/tex]
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,∞)
