Algebra 2 help! functions (composite of functions)

[an12345]

Let f(x)= 9x-2 and g(x)= -x+3. Find f(g(x)).

This is what I have so far:

g(x)= -x+3
f(g(x))= f(-x+3)
f(x)= 9x-2
f(g(x))= 9x-2( )
f(g(x))= 9x-2(-x+3) <--Here you have to multiply: 9x* -x, then 9x*3, then -2*-x, then -2*3.
f(g(x))= -9x^2+27-3x+6 <-- I am almost done but I don't know how to simplify it.

 

[srmichael]

Let f(x)= 9x-2 and g(x)= -x+3. Find f(g(x)).

This is what I have so far:

g(x)= -x+3
f(g(x))= f(-x+3)
f(x)= 9x-2
f(g(x))= 9x-2( )
f(g(x))= 9x-2(-x+3) <--Here you have to multiply: 9x* -x, then 9x*3, then -2*-x, then -2*3. ===> NO
f(g(x))= -9x^2+27-3x+6 <-- I am almost done but I don't know how to simplify it.

f(g(x)) in simple jargon is substitute the g(x) function for x in the f(x) function.

If I asked you to evaluate f(4), I'm sure you would know to just substitute 4 in for x in f(x) like this: 9(4) - 2.

Well, f(g(x)) = f(-x + 3) = 9(-x + 3) - 2 and then you can distribute and simplfy like normal.

Make sense?