Determine if an inverse function exists where the function f maps the real numbers to the real numbers by f(x) = $0.5(x+1)^3$ + 2.
I think an inverse function exists if and only if the function is bijective. I sketched the function and it is injective (one-to-one) due to the horizontal line test. To check whether it is surjective I checked whether the image of the graph was equal to the codomain, so the set of real numbers. I think it is, so I believe the inverse function exists.
Would this be correct ?