Find the inverse of the function f(x) = e^(3x - 5).

Any function f(x) and its inverse `f^-1(x)` follow the
relation: `f(f^-1(x)) = x` .

For the function `f(x) = e^(3x
- 5)` , to determine the inverse, we use the relation `f(f^-1(x)) = x`
.

`f(f^-1(x)) =
x`

`e^(3*f^-1(x) - 5) = x`

Now
take the logarithm to base e for both the sides.

`log_e
(e^(3*f^-1(x) - 5)) = log_e x`

Use the relation `log a^b =
b*log a` and `log_b b = 1`

`(3*f^-1(x) - 5)*log_e e = log_e
x`

`3*f^-1(x) - 5 = log_e
x`

`3*f^-1(x) - 5 = ln
x`

`3*f^-1(x) = 5 + ln
x`

`f^-1(x) = (5 + ln
x)/3`

The required inverse function is `f^-1(x) = (5 + ln
x)/3`