一道数学题，求解析，谢谢大佬

u =ⁿ√x；f(x) = (1/2)[ ( u^2 - 1 )/u ] =( u^2 - 1 )/(2u)；1 +f(x)^2 = 1 +( u^2 - 1 )^2/(2u)^2= [ 4u^2 +( u^2 - 1 )^2 ]/(2u)^2=( u^2 + 1 )^2 ]/(2u)^2；√[1 +f(x)^2 ] =( u^2 + 1 )/(2u)f(x) -√[1 +f(x)^2 ] =( u^2 - 1 )/(2u) -( u^2 + 1 )/(2u) = -2/(2u) = -1/u；故 g(f(x)) = { f(x) -√[ 1 + f(x)^2 ] }^n = (-1/u)^n = ( -1/ⁿ√x )^n = (-1)^n/x 。