Question

HELP, PLEASE! How do you graph f(g(x))? I'm really confused!

Answer 1

is there anymore to this question?
are you given a table of values? or are you given f(x) and g(x)?

Answer 2

I'm trying to understand in general how to approach this type of graphing if you could wal kmtr through a example that'd be great!

Answer 3

for example:
let f(x) = x^2 and g(x) = x
lets say u want to evaluate f(g(x)) at 3
so g(x) = 3
sp f(g(x)) = f(3) = 3^2 = 9

Answer 4

What I'm not understanding is how to plot this. That's where Im getting confused !

Answer 5

just evaluate the composition function at different values and plot the results

Answer 6

sure thing!
lets say that you are given 2 functions of x, f(x) and g(x)

\[f(x) = x^2 - x\]
\[g(x) = \sin(x)\]

the simplest way to graph f(g(x)) is to just solve for it, and then graph it.
f(g(x)) is just
\[f(x) = [g(x)]^2 - [g(x)]\]
and in order to get this you just substitute g(x) in for every x term you see in f(x).

g(x) is synonymous to sin(x), these terms can be interchanged.
so you end up with
\[f(g(x)) = [sinx]^2 - [sinx]\]
then you can draw a graph from there, or find any value of f(g(x))

Answer 7

How would I do that while looking at two graphed functions? Say I have a graph and I take the y value of a function, let's call it g(x). So then I use the y value as the x in f(x). How would I plot that point?

Answer 8

in my example for x=3, you got y=9...so plot tht (3,9)
now use something else instead of 3 and plot tht and so on

Answer 9

lets say u have 2 graphs and evaluating the first graph g(x) (inside function) at 3 gave u 4. so now evaluate f(x) (outside function) at 4

Answer 10

something like this?
find (f(g4))?