The function g:R→R defined by g(x)=x3+4x has an inverse on R. Which option correctly justifies this fact?
a) g is surjective onto R, therefore it is invertible.
b) Since g′(x) exists for every real x, g possesses an inverse function.
c) g is strictly increasing on R, hence one–one and invertible.
d) Because g(0)=0 and g′(0)=0, the inverse–function theorem guarantees that g is invertible on R.