What is the inverse of the function f(x) = (e^3x)*14 - 21

We'll suggest another method of getting the inverse
function.

We know that the product of derivative and it's inverse is
1.

f'(x)*[f^-1(x)]' =1

We'll divide
both sides by f'(x):

[f^-1(x)]' =
1/f'(x)

We'll calculate the integral of functions both
sides:

Int [f^-1(x)]'dx = Int
dx/f'(x)

We'll differentiate the function
f(x):

f'(x) = [(e^3x)*14 - 21]'

f'(x) =
42*e^3x

f^-1(x) = Int dx/42*e^3x

Int
dx/42*e^3x = (1/42)*Int e^-3xdx

Int dx/42*e^3x =
-e^-3x/3*42

Int dx/42*e^3x =
-1/126*e^3x

Therefore, the inverse function is:
f^-1(x) = -1/126*e^3x.