SOLUTION: Find Inverse of y=3e^x+5, Sketch graph of both functions..Trying to understand notes & work out, please show me the correct way. Thanks :)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find Inverse of y=3e^x+5, Sketch graph of both functions..Trying to understand notes & work out, please show me the correct way. Thanks :)      Log On


   

Question 727395: Find Inverse of y=3e^x+5, Sketch graph of both functions..Trying to understand notes & work out, please show me the correct way. Thanks :)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Express y in functional notation. f(x)=3e^x+5, and let g(x) be the inverse of f(x) so that f%28g%28x%29%29=3e%5E%28g%28x%29%29%2B5=x
3e%5E%28g%28x%29%29=x-5
e%5E%28g%28x%29%29=%28x-5%29%2F3
ln%28e%5E%28g%28x%29%29%29=ln%28x-5%29-ln%283%29
The inverse function, highlight%28g%28x%29=ln%28x-5%29-ln%283%29%29.

f(x) in red, g(x) in green
graph%28400%2C400%2C-3%2C20%2C-3%2C20%2C3e%5Ex%2B5%2Cln%28x-5%29-ln%283%29%29