Question

;Please help me understand how to do problems like these. Failed first part of algebra.
Let f(x) = 9x - 2 and g(x) = -x + 3. Find f(g(x)).

Answer 1

Alright...when you have this composite function...

f(g(x)) it means you deal with the inside function first...in this case g(x)

so

g(x) = -x + 3

We leave this alone however since we only want g(x) as opposed to g(2) or something etc..

So now we take that g(x) equation...and plug it into f(x) for every 'x' we see...

so

f(x) = 9x - 2

After replacing the 'x' with g(x) we have

f(g(x))= 9(-x + 3) - 2

Can you solve this from here?

Answer 2

hmm

Answer 3

o i get it now

Answer 4

thank you

Answer 5

Anytime :)

Just to be clear for similar cases...say you had the same 2 equations....but you want f(g(3))

Well you would do the same....focus on g(x) first

g(x) = -x + 3

But instead of g(x) we want g(3) so we replace every 'x' we see in g(x) with 3...

g(3) = -3 + 3
g(3) = 0

Then you would take your result (0 here) and plug THAT into f(x) for every 'x' you see...so

f(x) = 9x - 2

would become

f(0) = 9(0) - 2
f(0) = -2

Make sense?

Answer 6

i got -9x-2

Answer 7

c:

Answer 8

Not quite...

f(x) = 9(-x + 3) - 2

distributing the 9...

f(x) = -9x + 27 - 2

Simplify

f(x) = -9x + 25 <---is what I get

Answer 9

oh shoot.

Answer 10

well i also just did (-4+7) (10x-6) and got 5x -3

Answer 11

:/