is f(x) = 2(x + 5)3 + 1 is one to one. Is it also onto?

Question

Determine whether the function f(x) = 2(x + 5)3 + 1 is one to one. Is it
also onto? Please justify your answer.

Answer 1

Let y=f(x)=2(x+5)3+1=6x+31, therefore x=⅙(y-31). All values of y have a corresponding x value (linear relationship) so f(x) is 1-1 because x is associated with a unique value of y (and vice versa), and f(x) is onto because there is no value of y which has no corresponding x.