Given f(x)=ln (ex−2) + 3

Question

Given f(x)=ln (e^x−2) + 3

a) Find the domain and range of f(x).

b) State all the transformations of f(x).

c) Find f−1(x).

Answer 1

Simplify: f(x) = (x-2) + 3, so final simplification is x+1.

 

Domain: x can be any Real.

 

Range: any Real number.

 

Do you know how to find the inverse (by interchanging x & y, then solving for y, which is f^-1.  Easy for you to do.

 

The discussion(s) about transformation(s) seems irrelevant in light of the simplification that should be made.