Question 1084918
<pre><b><font size=4>
{{{g(x)}}}{{{""=""}}}{{{-1+log(2,(x-5))}}}

Replace g(x) by y

{{{y}}}{{{""=""}}}{{{-1+log(2,(x-5))}}}

Interchange x and y

{{{x}}}{{{""=""}}}{{{-1+log(2,(y-5))}}}

Solve for y

Add 1 to both sides

{{{x+1}}}{{{""=""}}}{{{log(2,(y-5))}}}

Use the definition of a logarithm:

{{{y-5}}}{{{""=""}}}{{{2^(x+1))}}}

Add 5 to both sides:

{{{y}}}{{{""=""}}}{{{5+2^(x+1))}}}

Replace y by g<sup>-1</sup>(x)

{{{g^(-1)}}}{{{(x)}}}{{{""=""}}}{{{5+2^(x+1)}}}

{{{drawing(400,400,-5,15,-5,15,
green(line(5,-30,5,30),line(-30,5,30,5)), 
graph(400,400,-5,15,-5,15,-1+ln(x-5)/ln(2)),
graph(400,400,-5,15,-5,15,30,28,27,29,31,x*sqrt(sin(5x))/sqrt(sin(5x))),
graph(400,400,-5,15,-5,15,25,26,5+2^(x+1))

  )}}}

The red graph is of g(x), the blue graph is of g<sup>-1</sup>(x).
The green lines are the asymptotes.  The asymptote for  
g(x) has equation x=5. The asymptote for g<sup>-1</sup>(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</pre></b></font>