Final answer:
To find the inverse of f(x) = x² + 7, replace f(x) with y and solve for x, resulting in the inverse function f–1(x) = √(x - 7), considering the domain x ≥ 7.
Step-by-step explanation:
To find the inverse function of f(x) = x² + 7, we must first replace f(x) with y, giving us y = x² + 7. To find the inverse, we solve for x. We start by subtracting 7 from both sides to get y - 7 = x². Taking the square root of both sides, we get x = ±√(y - 7).
Since the square root has two values (positive and negative), we choose the one that matches the domain and range of the original function. If f(x) is defined for all nonnegative values of x, the inverse would be f–1(x) = √(x - 7). If f(x) includes negative values of x, then we would consider both, resulting in two different functions.
However, because we're dealing with f(x) that implies only one output for each input without restrictions, we consider the principal square root. Thus, the equation for the inverse function is f–1(x) = √(x - 7), considering the domain where x is greater than or equal to 7.