If $f(x) = \left[ {4 - {{(x - 7)}^3}} \right],$ then ${f^{ - 1}}(x) =$……………

It is given that,, $f(x) = \left\{ {4 - {{(x - 7)}^3}} \right\}$

Let $y = \left[ {4 - {{(x - 7)}^3}} \right]$
${(x - 7)^3} = 4 - y$

$(x - 7) = {(4 - y)^{1/3}}$

$\Rightarrow$ $x = 7 + {(4 - y)^{1/3}}$

${f^{ - 1}}(x) = 7 + {(4 - x)^{1/3}}$