What is the inverse function for f(x) = 3*ln (2x-1) + 5.

The function f(x) = 3*ln (2x - 1) +
5

let y = f(x)

=> y =
3*ln (2x - 1) + 5

=> y - 5 = 3*ln (2x -
1)

=> (y - 5)/3 = ln (2x -
1)

=> 2x - 1 = e^[(y -
5)/3]

=> 2x = e^[(y - 5)/3] +
1

=> x = (e^[(y - 5)/3] +
1)/2

interchange x and
y

=> y = (e^[(x - 5)/3] +
1)/2

The inverse of f(x) is f^-1(x) = (e^[(x
- 5)/3] + 1)/2