Question

Given the function g(x) = 41x3 + a for some constant a, which describes the inverse function

Answer 1

Answer:

When we have a function g(x) such that:

g(x) = y.

Then the inverse, h(x), must be such that:

h(y) = x.

This means that:

g( h(x) ) = x

h( g(x) ) = x.

In this case, g(x) = 41*x^3 + a.

Then:

g( h(x)) = x = 41*h(x)^3 + a.

Now we can solve it for h(x).

             x - a = 41*h(x)^3

             (x - a)/41 = h(x)^3

            ∛( (x -a)/41 ) = h(x)

h(x) is the inverse function of g(x).