Question

Haile Homebuilder uses the function, f(x) = -100(x^2 – 750), to depreciate tiny homes, where f(x) is the value of the tiny house in dollars, and x is the number of years since the tiny house was built.

Part A: Write a formula for f^(-1)(x) for x = 20, and explain what it means in this situation.
Part B: Would the inverse function be used in a real-world situation? Explain your answer.

Answer 1

The formula for f^(-1)(x) for x = 20 is approximately 27.4, representing the number of years since the tiny house was built when the value of the tiny house is $20. In a real-world situation, the inverse function may not have a practical application.

Step-by-step explanation:

Part A:

To find the inverse function f^(-1)(x) for x = 20, we need to solve the equation f(x) = -100(x^2 - 750) = 20 for x. Let's do that:

-100(x^2 - 750) = 20

x^2 - 750 = -20/100

x^2 - 750 = -0.2

x^2 = 750 - 0.2

x^2 = 749.8

x = ±√749.8

Since x represents the number of years since the tiny house was built, we can take the positive square root:

x = √749.8 ≈ 27.4

Therefore, the formula for f^(-1)(x) for x = 20 is approximately 27.4.

Part B:

In a real-world situation, the inverse function may not have a practical application. In this case, f^(-1)(x) represents the number of years since the tiny house was built when the value of the tiny house is $20. This information might not be relevant or useful in most situations, so the inverse function may not be necessary to use.