a)
I think f has not an inverse, because f is not one-to-one function:
Question:
a) f(x) = | (3-x)/(x-2) |, x > 2
Define the inverse funtion of f corresponding to the domain of f.
b) g(x) = ln (x+2), x > -2
h(x) = 2 + (e ^ -x) , x > b and b > 0
The composite function gh is well defined and the range of gh is given as (ln 4, ln 6]. Find the exact value of b.
Thank you for helping me!
1. Write the equation of f as a piecewise defined function: (completely drawn in black)
2. Since f(3) = 0 this is the minimum of f. The behavior of the function changes at x = 3 from monotically decreasing to monotically increasing.
3. Therefore the inverse function must be defined piecewise too:
EDIT: As red_dog pointed out there doesn't exist one inverse function. Therefore you have to split my last answer into:
and