SOLUTION: f(x)=1/(x-4) g(x)=4x+9 find (f o g)(5)=? (f o g)(x)=?

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Question 1065645: f(x)=1/(x-4) g(x)=4x+9
find (f o g)(5)=?
(f o g)(x)=?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


f∘g(x) is read "f of (g of x)".

If means the same as f%28%22g%28x%29%22%5E%22%22%29

To get it, substitute what g(x) equals, for x in what
f(x) equals.  Then simplify.

We start with f(x)

f%28x%5E%22%22%29=1%2F%28x-4%29

Then we take what g(x) equals, which is (4x+9), and
substitute it for x in 1%2F%28x-4%29, like this: 1%2F%28%284x%2B9%29%5E%22%22-4%29

So we have:

f∘g(x) = f%28%22g%28x%29%22%5E%22%22%29%22%22=%22%22%22%22=%22%22f%284x%2B9%5E%22%22%29%22%22=%22%221%2F%28%284x%2B9%29%5E%22%22-4%29

Then we simplify

f∘g(x) = 1%2F%284x%2B9-4%29 

f∘g(x) = 1%2F%284x%2B5%29

That's the answer.

To find f∘g(5), we merely substitute 5 for x

f∘g(5) = 1%2F%284%285%29%2B5%29 and simplify

f∘g(5) = 1%2F%2820%2B5%29

f∘g(5) = 1%2F25

Be sure to watch this youtube video:

https://www.youtube.com/watch?v=S4AEZElTPDo

Edwin