SOLUTION: I am not understanding the (f o f) problems this one for sure f(x)=3x and g(x)=9x^2+1 with (f o f)(1) Thank you

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Question 1015736: I am not understanding the (f o f) problems this one for sure
f(x)=3x and g(x)=9x^2+1
with (f o f)(1)
Thank you

Found 2 solutions by fractalier, ikleyn:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
(f o f)(1) means f(f(1)).
f(1) = 3(1) = 3
f(3) = 3(3) = 9
so
(f o f)(1) = 9

Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
I am not understanding the (f o g) problems this one for sure
f(x)=3x and g(x)=9x^2+1
with (f o f)(1)
--------------------------------------------------------

Hello,

to find (fog)(x), you need to substitute the expression for g(x) into f(x) instead of x, 
and after that to make all necessary calculations / transformations.


It is the general rule, and below I show you how it works in your case.


Your function f(x) = 3*x simply multiplies x by 3.
Now, substitute g(x) into f instead of x. You will get


(fog)(x) = f( (g(x) ) = 3*g(x) = 3%2A%289x%5E2%2B1%29 = 27x%5E2+%2B+3.


That is all. You just found (f0g)(x). It is (fog)(x) = 27x%5E2+%2B+3.


Now, when they ask you about (fog)(1), simply substitute x=1 into 

(fog)(x) = 27x%5E2+%2B+3.

You will get (fog)(x) = 27%2A1%5E2+%2B+3 = 27 + 3 = 30.

It is your answer.

One more notice. What I wrote above, relates to (fog)(x) and (fog)(1).

It is not about (fof)(x) and not about (fof)(1).

Next time formulate your question more clearly please.
Here you mixed two questions: about (fog)(x) and about (fof)(x).