Question 529535

{{{f^(-1)(x) = root(3, (x+5)) }}} you refer to the inverse of the function f(x).  

Given {{{y = root(3, (x+5))}}}
 
to find an inverse of f(x) you will need interchange the {{{x}}} and {{{y}}}:  

{{{x = root(3, (y+5))}}}


now  solve for {{{y}}}:

To undo the cube root, you must cube both sides:

{{{x = (root(3, (y+5)))^3}}}

{{{x^3 = y+5 }}}

{{{x^3 - 5 = y}}}

or
{{{y=x^3 - 5 }}}

This new {{{y }}} that you just solved for the the inverse function for {{{f(x)}}}; so, the inverse function for {{{f(x) =root(3, (y+5)) }}} is {{{f^(-1) (x) = x^3 - 5 }}}