Precalculus (6th Edition)

$f(x)=x^{3}$ 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