Answer:
To find the inverse of the function f(x) = (x - 12)^2 on the domain [12, infinity), we can follow the steps below:
Step 1: Replace f(x) with y.
y = (x - 12)^2
Step 2: Swap the positions of x and y.
x = (y - 12)^2
Step 3: Solve for y.
Taking the square root of both sides, we get:
y - 12 = ±√x
Adding 12 to both sides, we get:
y = 12 ± √x
However, we are given that the domain of the inverse function is [12, infinity). Since the expression 12 - √x is negative for x > 144, we must choose the positive square root to satisfy the given domain. Therefore, the inverse function is:
f^-1(x) = 12 + √x, x ≥ 144
Note that we have restricted the domain of the inverse function to [144, infinity) to ensure that the function is one-to-one and has a unique inverse.