Answer
$(f^{-1}~o~g^{-1})(-1)=32$
Work Step by Step
$f(x)=\frac{1}{8}x-3$
$y=\frac{1}{8}x-3~~$ (Interchange $x$ and $y$):
$x=\frac{1}{8}y-3$
$x+3=\frac{1}{8}y$
$y=8x+24$
$f^{-1}(x)=8x+24$
$g(x)=x^3$
$y=x^3~~$ (Interchange $x$ and $y$):
$x=y^3$
$y=\sqrt[3] x$
$g^{-1}(x)=\sqrt[3] x$
$(f^{-1}~o~g^{-1})(-1)=f^{-1}(g^{-1}(1))=f^{-1}(\sqrt[3] 1)=f^{-1}(1)=8(1)+24=32$
