find the inverse function of c(x)=3+ln(4-x)?

let c (x) = 3 + ln (4 - x) = y and g (y) = x
g is inverse of c

ln (4 - x) = y - 3
4 - x = e^(y - 3)
x = 4 - e^(y - 3)
g (y) = 4 - e^(y - 3)
g (x) = 4 - e^(x - 3)____inverse function

Replace c(x) with y temporarily for convenience.
y = 3 + ln(4 -x )
Swap x's and y's and solve for y.
x = 3 + ln(4 - y)
x - 3 = ln(4 - y)
e^(x - 3) = 4 - y
e^(x - 3) - 4 = y
c^-1(x) = e^(x - 3) - 4