SOLUTION: Express the function y = 9 (x - 4)^{4} as a composition y = f(g(x)) of two simpler functions y = f(u) and u = g(x)

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Question 800690: Express the function y = 9 (x - 4)^{4} as a composition y = f(g(x)) of two simpler functions y = f(u) and u = g(x)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Try to decompose the composition of y.

Maybe assign u=x-4. This can allow to say, y=9u%5E4. The function that takes u as an input is something%28t%29=9t%5E4.

u=g(x), and something(t) has been given g(x) as input, so you have like, something%28g%28x%29%29=y. That was a name just used for planning. We can call "something", as f.

f%28g%28x%29%29 is the composition f o g where f%28x%29=9x%5E4 and g%28x%29=x-4

That may seem twisted to think through, but normally we start from the other direction in academic exercises, given functions, told something about the composition, and then form the composition and do something with one or the other or evaluate the composition at some value of x.