(Solution) - Let f x 3x 2 x2 1 -(2025 Original AI-Free Solution)

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Let f(x) = 3x + 2 / x2 + 1 and g(x) = 1/ 100 cos (100x).
(a) Use functional composition to form h(x) = (f ? g) (x), as well as j(x) = (g ? f) (x).
(b) Find the appropriate window or windows that give a clear picture of h(x).
(c) Find the appropriate window or windows that give a clear picture of j(x).
Indicate briefly which (x, y)-window shows the true behavior of the function and discuss reasons why the other (x, y)-windows give results that look different. In this case, it true that only one window gives the important behavior, or do we need more than One window to graphically communicate the behavior of this function?