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For the function f(x) = 3√(6x), find ƒ−¹(x).

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To find the inverse of the function f(x) = 3√(6x), we can follow these steps:

Step 1: Replace f(x) with y: y = 3√(6x).

Step 2: Swap the variables x and y: x = 3√(6y).

Step 3: Solve for y in terms of x. To do this, we'll isolate the radical term:

x = 3√(6y)

x/3 = √(6y)

(x/3)^2 = 6y

(x^2)/9 = 6y

y = (x^2)/54

Step 4: Replace y with ƒ^(-1)(x): ƒ^(-1)(x) = (x^2)/54.

Therefore, the inverse function of f(x) = 3√(6x) is ƒ^(-1)(x) = (x^2)/54.

User JojoIV
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