show  f(f-1(x)) = x for the given function f(x) = x5+4

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Let y=f(x)=x⁵+4. x⁵=y-4, x=(y-4)^⅕. Let g(y)=x=(y-4)^⅕. So g(x)=(x-4)^⅕. And g(x)=f⁻¹(x), by definition of inverse function.

f(f⁻¹(x))=f(g(x))=(g(x))⁵+4=((x-4)^⅕)⁵+4=x-4+4=x.

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