Final answer:
The inverse function of f(x) = (x - 5)² for x ≥ 5 is g(x) = √x + 5, where we consider only the positive square root due to the given domain of the original function.
Step-by-step explanation:
The student has asked to find the inverse function of f(x) = (x - 5)² for x ≥ 5, where function g is the inverse of function f. To find the inverse of a function, we need to switch the roles of x and y in the equation and solve for y. Since we are only considering x ≥ 5, we avoid the negative square root to maintain the function's definition.
Step 1: Replace f(x) with y: y = (x - 5)².
Step 2: Replace y with x to find g(x): x = (y - 5)².
Step 3: Take the square root of both sides, remembering to consider only the positive root since x ≥ 5: √x = y - 5.
Step 4: Solve for y to get the inverse function: y = √x + 5.
So, the inverse function g(x) is g(x) = √x + 5.