Question 1169488
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{{{ y = 3x^3-9 }}}

General strategy: solve for x then swap x & y at the very end.

{{{ y+9 = 3x^3 }}}              <--- added 9 to both sides
{{{ (y+9)/3 = x^3 }}}           <--- divided both sides by 3
{{{ root(3,((y+9)/3)) = x }}}   <--- took cube root of both sides

{{{ x = root(3,((y+9)/3)) }}}   <--- re-wrote w/x on left hand side

Now swap x & y:
{{{ highlight( y = root(3, ((x+9)/3)) ) }}}  <--- this is the inverse function


Check...
You can check it by computing {{{ f^-1(f(x)) }}} ... it should give you x back.
We plug in '{{{ (3x^3-9) }}}' for 'x' in the inverse function:
{{{ f^-1(f(x)) = root(3,((3x^3-9) + 9)/3) = root(3,(3x^3/3)) = x}}} (ok)