Question 1065645
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f&#8728;g(x) is read "f of (g of x)".

If means the same as {{{f("g(x)"^"")}}}

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

We start with f(x)

{{{f(x^"")=1/(x-4)}}}

Then we take what g(x) equals, which is (4x+9), and
substitute it for x in {{{1/(x-4)}}}, like this: {{{1/((4x+9)^""-4)}}}

So we have:

f&#8728;g(x) = {{{f("g(x)"^"")}}}{{{""=""}}}{{{""=""}}}{{{f(4x+9^"")}}}{{{""=""}}}{{{1/((4x+9)^""-4)}}}

Then we simplify

f&#8728;g(x) = {{{1/(4x+9-4)}}} 

f&#8728;g(x) = {{{1/(4x+5)}}}

That's the answer.

To find f&#8728;g(5), we merely substitute 5 for x

f&#8728;g(5) = {{{1/(4(5)+5)}}} and simplify

f&#8728;g(5) = {{{1/(20+5)}}}

f&#8728;g(5) = {{{1/25}}}

Be sure to watch this youtube video:

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

Edwin</pre></b></font>