Final answer:
To find the inverse of the function f(x) = 3(x-3)^2+1 for x ≥ 3, swap the x and y variables and solve for y. The inverse function is f^(-1)(x) = √((x - 1)/3) + 3.
Step-by-step explanation:
To find the inverse of the function f(x) = 3(x-3)^2+1 for x ≥ 3, we need to swap the x and y variables and solve for y. First, we can write the equation as x = 3(y-3)^2+1. Then, we can solve for y by isolating the variable.
Step 1: Subtract 1 from both sides to get x - 1 = 3(y-3)^2.
Step 2: Divide both sides by 3 to get (x - 1)/3 = (y-3)^2.
Step 3: Take the square root of both sides to get √((x - 1)/3) = y-3.
Step 4: Add 3 to both sides to get √((x - 1)/3) + 3 = y.
So, the inverse function of f(x) = 3(x-3)^2+1 for x ≥ 3 is f^(-1)(x) = √((x - 1)/3) + 3.
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