Final answer:
To verify if the given function is the inverse of f(x), we must check if applying one function to the other yields the identity function, resulting in x. The student's original expression seems to have a typo and should more likely be g(x) = (-3+x)³ √(x+4). Without the correct expression, we cannot conclude whether it is the inverse function.
Step-by-step explanation:
To determine if the given function (3) = (-3+1)³ √(x+4) is the inverse function of f(x) = (x-3)³ + 4, we need to check if composing one function with the other gives us the identity function, which is defined as f(g(x)) = g(f(x)) = x. This involves plugging one function into the other and simplifying to see if the result equals x.
In this case, we need to correctly interpret the first expression. The student likely meant to write g(x) = (-3+x)³ √(x+4). To check if g(x) is the inverse of f(x), we would substitute x from f(x) into g(x) and verify if g(f(x)) simplifies to x. Additionally, we would need to perform the check the other way to ensure that f(g(x)) also simplifies to x. Without the correct expression for g(x), we cannot accurately complete this check.