Determine Whether or Not the Function $h ( x ) = 3 x ^ { 6 } + 2$

question 64

Essay

Determine whether or not the function $h ( x ) = 3 x ^ { 6 } + 2$ , $0 \leq x \leq \infty$ is one-to-one.

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Definitions:

Porta Marzia

An ancient Etruscan gate located in Perugia, Italy, notable for its monumental structure and sculptural decorations, dating back to the 3rd century BCE.

Etrusco-Roman

Pertaining to the cultural, art, and historical amalgamation characteristics observed between the Etruscans and the Romans.

Pilaster

A flat, rectangular, vertical member projecting from a wall of which it forms a part. It usually has a base and a capital and is often fluted.

Regolini-Galassi Tomb

An ancient Etruscan tomb discovered in Cerveteri, Italy, known for its rich grave goods and insights into Etruscan culture and burial practices.