Determine whether or not the function is one-to-one.
-$$f ( x ) = 2 x ^ { 3 } - 5$$
A) Yes
B) $\mathrm { No }$

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 given function $f(x) = 2x^3 - 5$ is a cubic function, which is known to be one-to-one because its derivative $f'(x) = 6x^2$ is always positive for $x > 0$ and always negative for $x < 0$, except for a single point at $x = 0$ where it is $0$. This means the function is always increasing or decreasing, ensuring it passes the horizontal line test for being one-to-one.

Determine Whether or Not the Function Is One-To-One f(x)=2x3−5f ( x ) = 2 x ^ { 3 } - 5f(x)=2x3−5

Determine Whether or Not the Function Is One-To-One $f ( x ) = 2 x ^ { 3 } - 5$