#### Answer

one-to-one

#### Work Step by Step

$f(x)=x^{3}$ is a one-to-one function, and its inverse is $g(x)=\sqrt[3]{x},$(which is also one-to-one)
The graph of g(x) is obtained by reflecting f(x) about the line y=x.
The graph of $y=\sqrt[3]{x+1}-3$ is obtained from g(x) by
- shifting it left by one unit, and
- shifting down by three units.
This graph passes the Horizontal Line Test, so the function is one-to-one