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 $(gof)^{-1}(\frac{1}{4})$ is equal to _____.

$(gof)^{-1}(\frac{1}{4})=(f^{-1}og^{-1})(\frac{1}{4})=f^{-1}(g^{-1}(\frac{1}{4}))=f^{-1}(1)=4$.