Precalculus · Problem 5.1.43

Further Topics in Functions — Stitz & Zeager

Mathematics — Precalculus · function-decomposition-linear-transforms

Problem

What linear functions could be used to transform

f(x) = x^3

into

F(x) = -\dfrac{1}{2}(2x - 7)^3 + 1

? What is the proper order of composition?