y = 2x^3 + 1
y - 1 = 2x^3
(y-1)/2 = x^3
( (y-1) / 2 ) ^ (1/3) = x
Inverse: y = ( (x-1) / 2 ) ^ (1/3)
The inverse is a function because, for each value of x, there is only one value of y.
This is another way of saying it passes the vertical line test- for each possible value of x, a vertical line only crosses the function once.