Question

Inverse functions w/ logarithms.
If g(x) = 3 + x + e^x, find g-1(4)

I know that to set it up we do something akin to
g(x) = 3 + x + e^x
y = 3 + x + e^x
x + e^x = y - 3
here is where I'm confused on what to do.
do I take the natural log of everywhere, giving me,
ln x + x = ln (y-3)? I don't know how to single out the x's.

Answer 1

g(x)=y=3+x+(e^x)
in order to get inverse of y interchange x and y
so we have x=3+y+e^y
=> y+e^y=x-3 eqn 1
from above we can get get g-1(x) as function of x
now we have to find g-1(4) so place x=4 in eqn 1
we get y+e^y=1
we know that e^0=1
so g-1(4)=0 Ans
I hope the solution is explained properly