Question 844373
<pre>{{{"f(x)"}}}{{{""=""}}}{{{log(3,(x+1))}}}


Change f(x) to y

{{{y}}}{{{""=""}}}{{{log(3,(x+1))}}}

Interchange x and y

{{{x}}}{{{""=""}}}{{{log(3,(y+1))}}}

Use the principle that {{{A=log(B,(C))}}} is equivalent to {{{C=B^A}}} 

{{{y+1}}}{{{""=""}}}{{{3^x}}}

Solve for y:

{{{y}}}{{{""=""}}}{{{3^x-1}}}

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

f<sup>-1</sup>(x) = 3<sup>x</sup> - 1 

So substitute x=2

f<sup>-1</sup>(2) = 3<sup>2</sup> - 1 = 9 - 1 = 8

Edwin</pre>