find the two functions which are the inverse of the functions

1/(1+x^2), x is equal to and > 0 AND 1/(1+x^2), x is equal to and <0

show that the following pairs of functions are inverses by showing that

f(g(x)) = g(f(x)) = x

f(x) = sqrt(16-x^2) -4<x<0 (x also equals -4 and 0)

g(x) = - sqrt(16-x^2), 0<x<4 (x also equals 0 and 4)

thank you so much for any help given !!!