f(x)=6x-1

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f(x)=6x-1

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Given f(x) = 6x -1 , find f^{-1}(x)

First, let f(x) = y

y = 6x - 1

Replace every x with y and every y with x:

x = 6y - 1

Solving this equation for y given you the inverse of the original function f(x):

x + 1 = 6y - 1 + 1

x + 1 = 6y

(x + 1)/6 = (6y)/6

(x + 1)/6 = y

Thus,

f^{-1}(x) = (x + 1)/6

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