Question

For RX = 11/(x-4)², what represents a domain restriction on RX in the corresponding inverse function?

a) x ≠ 4
b) x > 4
c) x < 4
d) No domain restriction

Answer 1

The domain restriction on the inverse function of RX = 11/(x-4)² is x ≠ 4. To find the inverse function, we switch the roles of x and y and solve for y. The domain restriction occurs when the original function RX has a value that would result in division by zero. The correct answer is option A .

Step-by-step explanation:

The domain restriction on the inverse function of RX = 11/(x-4)² is a) x ≠ 4. The inverse function, denoted by R⁻X, is the function that undoes the operation of RX. To find the inverse function, we switch the roles of x and y and solve for y. In this case, to find R⁻X, we will solve the equation x = 11/(y-4)² for y.

To solve for y, we can start by multiplying both sides of the equation by (y-4)² to get rid of the denominator. This gives us x(y-4)² = 11. Next, we can divide both sides of the equation by x to isolate the squared term. This gives us (y-4)² = 11/x. Finally, we can take the square root of both sides of the equation to solve for y. Note that when we take the square root, we need to consider both the positive and negative square root.

The domain restriction on the inverse function occurs when the original function RX has a value that would result in division by zero. In this case, RX is undefined when x-4 = 0, which means x = 4. Therefore, the domain restriction on the inverse function R⁻X is x ≠ 4.