Question

If R(8,infinity) defined by f(x)=x²+8,then what is f⁻¹(x)

Answer 1

The inverse function, f⁻¹(x), of the function f(x) = x² + 8 for the domain R(8, infinity) is √(x - 8) for x ≥ 8.

Step-by-step explanation:

The student is asking how to find the inverse function, denoted as f⁻¹(x), of the given function f(x) = x² + 8 for the domain R(8,infinity). To find f⁻¹(x), we need to express x in terms of y and solve for y. Given the equation y = x² + 8, we proceed as follows:

• Subtract 8 from both sides to obtain y - 8 = x²
• Since x is only taking values from 8 to infinity, x is positive, and so we can take the positive square root of both sides to solve for x
• This gives us x = √(y - 8)

Thus, the inverse function f⁻¹(x) is given by f⁻¹(x) = √(x - 8) when x ≥ 8.

The domain here is important because the inverse does not exist for x < 8 due to the original function's domain restriction.