If g(x) = 5 + x + e^(x), find g^(-1)(6).?

Question

I have to find the inverse of the function and solve for g but I always get stumped when it involved e^(x)

Answer 1

y=5+x+e^x

x = 5+y+e^y

x-5 = y+e^y

(x-5)/y = e^y

ln (x-5) - ln (y) = y

ln (x-5) - ln (5+x+e^x) =y

f^-1(x) = ln (x-5) - ln (5+x+e^x)

f^-1(x) = ln [ (x-5) / (5+x+e^x)]

f^(-6) = ln [ 1 / 11+e^6] =ln (0.0024129598)

= -6.0269

Answer 2

What the :O