Given the function g(x) = 41x3 + a for some constant a, which describes the inverse function g–1(x)? no restriction on the domain of g(x); inverse is g–1(x) = RootIndex 3 StartRoot StartFraction x minus a Over 41 EndFraction EndRoot
no restriction on the domain of g(x); inverse is g–1(x) = (StartFraction x minus a Over 41 EndFraction) cubed
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) = RootIndex 3 StartRoot StartFraction x minus a Over 41 EndFraction EndRoot
domain of g(x) restricted to x ≥ 0; inverse is g–1(x) = (StartFraction x minus a Over 41 EndFraction) cubed

A. No restriction on the domain of g(x); inverse is g–1(x) = RootIndex 3 StartRoot StartFraction x minus a Over 41 EndFraction EndRoot

Explanation:

Given the function , we are to find the inverse of the function a shown below:

Ley y = g(x)

replace y with x

make y the subject of the formula:

Replace y with

Hence the inverse function

No restriction on the domain of g(x). Hence the correct option is A

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