Final answer:
The domain restrictions of the expression (y²-3y-40)/(y²+9y+20) are y ≠ -5 and y ≠ -4, which correspond to the correct answer choices b and f from the provided options. These restrictions arise from setting the denominator equal to zero and solving for y.
Step-by-step explanation:
To determine the domain restrictions of the rational expression (y²-3y-40)/(y²+9y+20), we must set the denominator equal to zero and solve for y. This is because division by zero is undefined in mathematics, which would make the expression undefined at those points.
Let's factor the denominator:
- y² + 9y + 20 = (y + 5)(y + 4)
Setting each factor equal to zero gives us the values that y cannot be:
- y + 5 = 0 → y = -5
- y + 4 = 0 → y = -4
Therefore, the domain restrictions are y ≠ -5 and y ≠ -4. This means the correct options from the given are b. y ≠ -5 and f. y ≠ -4. Any other value that does not satisfy y² + 9y + 20 = 0 is not a restriction to the domain.
Now, let's check the answers provided to the question:
- a. y ≠ -8 is incorrect because -8 is not a solution to the denominator equaling zero.
- b. y ≠ -5 is correct.
- c. y ≠ 8 is incorrect because 8 is not a solution to the denominator equaling zero.
- d. y ≠ 5 is incorrect because 5 is not a solution to the denominator equaling zero.
- e. y ≠ 4 is incorrect because 4 is not a solution to the denominator equaling zero.
- f. y ≠ -4 is correct.