Replace g(x) by y



Interchange x and y



Solve for y

Add 1 to both sides



Use the definition of a logarithm:



Add 5 to both sides:



Replace y by g-1(x)





The red graph is of g(x), the blue graph is of g-1(x).
The green lines are the asymptotes.  The asymptote for  
g(x) has equation x=5. The asymptote for g-1(x) has 
equation y=5.  The faint blue dotted line is the graph 
of the identity function y=x.  The graph of the inverse 
of any function is the reflection of its graph across 
this identity line y=x.

Edwin