Final answer:
The inverse of the function f(x) = (x - 5)² for x ≥ 5 is g(x) = √(x) + 5, where g is the inverse of f.
Step-by-step explanation:
The function you have described is f(x) = (x - 5)² for x ≥ 5. To find the inverse of this function, we need to switch the roles of 'x' and 'y' and solve for the new 'x'. Starting with y = (x - 5)², we switch 'x' and 'y' to get x = (y - 5)². Since we are looking for the inverse for x ≥ 5, we consider the square root to be positive, and thus we can rewrite it as y - 5 = √(x) and then solve for 'y' to find the inverse g(x). This yields y = √(x) + 5. Therefore, the inverse function g(x) for x ≥ 5 is g(x) = √(x) + 5.