Let f = {(1, −1), (4, −2), (9, −3), (16, 4)}

f = {(1, −1), (4, −2), (9, −3), (16, 4)} and g = {(−1, −2), (−2, −4), (−3, −6), (4, 8)}

$f:\{1,4,9,16\} \rightarrow\{-1,-2,-3,4\}$ and $g:\{-1,-2,-3,4\} \rightarrow\{-2,-4,-6,8\}$

Co-domain of f = domain of g

So, gof exists and gof: $\{1,4,9,16\} \rightarrow\{-2,-4,-6,8\}$

$(g o f)(1)=g(f(1))=g(-1)=-2$

$(g o f)(4)=g(f(4))=g(-2)=-4$

$(g o f)(9)=g(f(9))=g(-3)=-6$

$(g o f)(16)=g(f(16))=g(4)=8$

So, gof $=\{(1,-2),(4,-4),(9,-6),(16,8)\}$

But the co-domain of g is not same as the domain of f.
So, fog does not exist.