SOLUTION: Find the inverse of the following function. find the domain, range and asymptotes of each function. graph both functions on the same coordinate plane. f(x)=ln(8-x) thanks :)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the inverse of the following function. find the domain, range and asymptotes of each function. graph both functions on the same coordinate plane. f(x)=ln(8-x) thanks :)      Log On


   

Question 712297: Find the inverse of the following function. find the domain, range and asymptotes of each function. graph both functions on the same coordinate plane.
f(x)=ln(8-x)
thanks :)
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
We look for another function g(x) so that g(f(x))=f(g(x))=x.

Considering the given function f(x)=ln(8-x), use g(x) as input:
f(g(x))=ln(8-g(x))=x, because we want f and g to be inverses.

ln%288-g%28x%29%29=x
e%5Ex=8-g%28x%29
e%5Ex-8=-g%28x%29
8-e%5Ex=g%28x%29
or
g%28x%29=8-e%5Ex, the inverse of f%28x%29=ln%288-x%29.

g(x)=8-e^x, graph:
graph%28550%2C550%2C-20%2C20%2C-20%2C20%2C8-e%5Ex%29