Final answer:
The broad set of ideas established by Lamarck, Lyell, and Darwin is that Earth and its life are ancient and ever-changing, with fossils documenting the evolution of life-forms over time.
Step-by-step explanation:
The work of Jean-Baptiste Lamarck, Charles Lyell, and Charles Darwin established a broad set of ideas that fundamentally changed our understanding of biology and geology. The correct answer to the question is c. Earth and its life are ancient and ever-changing; fossils document the evolution of life-forms over time. Lamarck proposed that organisms could acquire traits during their lifetime and pass these on to their offspring, a notion later disproven. However, Lamarck's work did contribute to evolutionary thought. Lyell's geological studies suggested a much older Earth, making room for the gradual processes of change that Darwin would later define in his theory of evolution by natural selection.
Charles Darwin's contributions synthesized many of these ideas, showing through his observations and the fossil record that life forms adapt to their environments and change over time. Darwin's observations on the Voyage of the Beagle, particularly in the Galapagos Islands, led him to propose that species evolve through natural selection, where favorable traits are passed on and become common within a population. This was a marked shift from the belief in fixed, unchanging species on a young Earth to a recognition of the deep history of life's evolution.