Determine whether the function is one-to-one.
-$$f ( x ) = 3 x ^ { 3 } - 8$$

Question

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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 given function $f(x) = 3x^3 - 8$ is a cubic function, which is known to be one-to-one because its derivative $f'(x) = 9x^2$ is always non-negative for all x (and never zero for all x except at a single point), indicating that the function is always increasing or decreasing, thus passing the Horizontal Line Test for being one-to-one.

Determine Whether the Function Is One-To-One f(x)=3x3−8f ( x ) = 3 x ^ { 3 } - 8f(x)=3x3−8

Determine Whether the Function Is One-To-One $f ( x ) = 3 x ^ { 3 } - 8$