Determine Whether or Not the Function $h ( x ) = x ^ { 3 } - x$

question 54

Essay

Determine whether or not the function $h ( x ) = x ^ { 3 } - x$ is one-to-one.

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Definitions:

Inflammation

A bodily response to injury or infection, characterized by redness, swelling, heat, and pain.

Osmotic Balance

The equilibrium achieved when the concentration of solutes and the movement of water are equal across a semipermeable membrane, essential for cell survival.

Migration

The movement of organisms from one place to another, often seasonally or following a lifecycle pattern.

Edema

A medical condition characterized by the accumulation of fluid in the body's tissues, leading to swelling.