Determine whether the function is one-to-one.
-$$f ( x ) = x ^ { 3 } - 7$$

Question

Quizplus · Accepted Answer

A function is one-to-one if each x-value corresponds to exactly one y-value and each y-value corresponds to exactly one x-value. The function $f(x) = x^3 - 7$ is a cubic function, which is known to be one-to-one because its derivative $f'(x) = 3x^2$ is always positive or negative except at $x = 0$, indicating it is always increasing or decreasing, thus passing the Horizontal Line Test.

Determine Whether the Function Is One-To-One f(x)=x3−7f ( x ) = x ^ { 3 } - 7f(x)=x3−7

Determine Whether the Function Is One-To-One $f ( x ) = x ^ { 3 } - 7$