Question

find f^-1 for the function f(x)=3sqrt 2x-1

Answer 1

To find the inverse of f(x) = 3√(2x-1), we can follow these steps:

Step 1: Replace f(x) with y: y = 3√(2x-1)

Step 2: Swap x and y: x = 3√(2y-1)

Step 3: Solve for y:

x = 3√(2y-1)

Cube both sides:

x^3 = (3√(2y-1))^3

x^3 = 27(2y-1)

Divide both sides by 27:

(1/27)(x^3) = (2y-1)

(1/27)(x^3) + 1 = 2y

Divide both sides by 2:

(1/54)(x^3) + 1/2 = y

Step 4: Replace y with f^(-1)(x): f^(-1)(x) = (1/54)(x^3) + 1/2

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