Question

Which equation is the inverse of (5y + 4 = (x + 3)² + 1/2)?

a) (y = √x - 11/2)

b) (y = √x - 2)

c) (y = (x - 3)² - 3/2)

d) (y = (x - 3)² + 3/2)

Answer 1

To find the inverse function, one must solve the given equation for y, exchange x and y, and then solve the new equation for y. However, the provided answer choices do not correspond with the solved inverse of the original equation.

Step-by-step explanation:

To find the inverse of the given equation (5y + 4 = (x + 3)2 + 1/2), we need to solve for y in terms of x, and then interchange x and y.

1. First, move 4 to the other side by subtracting it from both sides: 5y = (x + 3)2 - 7/2.
2. Next, divide by 5 to solve for y: y = ((x + 3)2 - 7/2) / 5.
3. After simplifying, interchange x and y to get the inverse: x = ((y + 3)2 - 7/2) / 5.
4. Finally, solve this new equation for y to find the inverse function.

Unfortunately, none of the answer choices provided (a) to (d) mathematically match the correctly solved inverse of the original equation. This could be due to a possible mistake in the question or the answer choices provided.