Question

The area of a rectangular carpet is given by the quadratic function A(x) = x(x + 30), where A(x) is the area and x is the width of the carpet in feet. What are the restrictions on the domain of the function and its inverse?

Answer 1

The inverse of the function is; f⁻¹(x) = - 15 ± √(x + 225)

What is the Inverse of the Function?

We have been given a quadratic function f(x) =  x(x + 30) and we need to restrict the domain such that it becomes a one to one function.

Now, the given function can also be written in vertex form as;

f(x) = (x + 15)² - 225

We know that vertex of this quadratic function occurs at (-15, -225).

Further, we know that range of this function is (-225, ∞).

If we restrict the domain of this function to either (-∞, -225) or (-225, ∞) , it will become one to one function.

Let us know find its inverse;

y =  (x + 15)² - 225

Upon interchanging x and y, we get:

x =  (y + 15)² - 225

Solving for y gives;

y = - 15 ± √(x + 225)

Thus, the inverse of the function is;

f⁻¹(x) = - 15 ± √(x + 225)

Read more about Inverse of a Function at; brainly.com/question/11735394

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