Question

attaching graph
PLEASE HELP EXAM TOMORROW
(last question)

Answer 1

can't wait to see this one

Answer 2

different procedure, same idea
lets do \[f\circ g(-4)\]

Answer 3

first we need \(g(-4)\) which you get from the graph
what it it?

Answer 4

if it is not clear, let me know, but it looks like you got this idea last time

Answer 5

0

Answer 6

ok good
next we need \(f(0)\)

Answer 7

why f(0)?

Answer 8

once you find it i will explain clearly

Answer 9

2

Answer 10

ok right
so what does \((f\circ g)(x)\) mean?
it means
\[f(g(x))\] without the circle notation
that means
\[(f\circ g)(-4)=f(g(-4))=f(0)=2\]

Answer 11

not sure if that was clear as needed, but that is what it means, first find g of the number, then find f of the result
want to try the next one?

Answer 12

so because -4 is at 0 thats f(0)?

Answer 13

yes because \(g(-4)=0\) then \(f(g(-4))=f(0)\)

Answer 14

which in this case is \(f(0)=2\) so that is your "final answer"

Answer 15

oh okay i see

Answer 16

want to try the next one see if it is clear?

Answer 17

yea, one question though. so g(x) will be x and f(x) will be y?

Answer 18

yeah that is sort of one way to think about it

Answer 19

oh wait nevermind

Answer 20

it is really
\[(f\circ g)(x)=f(g(x))\] so you need to compute \(g(x)\) first then take \(f\) of that result

Answer 21

is the next one 4 then?

Answer 22

hold on let me check with the picture

Answer 23

yes you got it
\[f(g(-6))=f(2)=4\]

Answer 24

for the following two it the other way
\[(g\circ f)(x)=g(f(x))\] so first \(f\) then \(g\) of that

Answer 25

-5

Answer 26

i got it :) thanks!

Answer 27

yw
good luck on the exam