Question 1132798
The general steps are:

Let y = f(x), solve for x, then swap the roles of x and y (literally swap the letters) and you will have  y = g(x)  where g(x) is the inverse of f(x).


  {{{ y = 3+(x+2)^5 }}}
  {{{ y - 3 = (x+2)^5 }}}
  {{{ root(5,(y - 3)) = (x + 2) }}}
  {{{ (root(5,(y - 3))) - 2 = x }}}<br>

Inverse of {{{ 3+(x+2)^5 }}} is therefore:
{{{  highlight( y = (root(5,(x-3))) - 2 ) }}} <br>

Check:
g(f(x)) = x  should hold true if g(x) is the inverse of f(x):

Substitute {{{ 3+(x+2)^5 }}} for "x" in the answer given:
{{{ (root(5,(3+(x+2)^5)-3)) - 2 }}} =<br>
{{{ (root(5,(x+2)^5))-2 }}} =<br>
{{{  (x+2)-2 }}} =<br>
{{{ x }}}