If $f: \{1, 2, 3, 4\}→\{1, 4, 9, 16\}$ and $g:\{1, 4, 9, 16\}→\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4}\}$ are two bijective functions such that $x_1>x_2>⇒f(x_1) <f(x_2), g(x_1) >g (x_2)$, then $f^{-1}(g^{-1}(\frac{1}{2}))$ is equal to _____.

Clearly, f is decreasing and g is increasing.

$∴ f(1) =16, f(2) = 9, f(3) = 4$ and $f(4) =1$

and, $g(x)=\frac{1}{4},g(4)=\frac{1}{3},g(9)=\frac{1}{2}$ and $g(16)=1$

$∴f^{-1}(g^{-1}(\frac{1}{2}))=f^{-1}(9)=2$