SOLUTION: Find f composed of g composed of h. f(x) = x + 1, g(x) = 5x, h(x) = x − 8

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Question 647171: Find f composed of g composed of h.
f(x) = x + 1, g(x) = 5x, h(x) = x − 8

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x + 1, g(x) = 5x, h(x) = x − 8
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f{g{h(x)]] = f[g[x-8)]] = f[5x-40] = 5x-40+1 = 5x-39
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Cheers,
Stan H.
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Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find f composed of g composed of h.
f(x) = x+1, g(x) = 5x, h(x) = x-8
f०g०h(x) means f⟨g[h(x)]⟩

We find what's inside the ⟨ ⟩ first, which is g[h(x)]

To get g[h(x)] we take the right side of g(x), which is 5x, and substitute
the right side of h(x), which is x-8 in place of x.

So we substitute x-8 into 5x, in place of x, and get 5(x-8), 
so now we have

     g[h(x)]⟩ = 5(x-8)

Now to get f⟨g[h(x)]⟩ we take the right side of f(x), which is x+1, and 
substitute the right side of g[h(x)]⟩, which is 5(x-8) in place of x.

So we substitute 5(x-8) into x+1, in place of x, and get 5(x-8)+1, 
so now we have

     f⟨g[h(x)]⟩ = 5(x-8)+1

and that's actually the answer, and we simplify it to 5x-40+1 = 5x-39,
so we write:

    f०g०h(x) = 5x-39

Edwin