Question

How would you find the range of f(x)=1-ln(x-2) ?

Answer 1

This is a transformation of a log function. Do you know what the range of a basic log function is? If you know what the graph of y=lnx looks like, then it should be fairly obvious what the range of this function is. :)

Answer 2

Here, you take y=ln(x) and:
-shift 2 units right
-reflect over x-axis
-shift up 1 unit

Will any of those change the range, as compared to the original function, y=ln(x)?