Question

I'm studying for a pre-calculus test and I dont really understand Composite functions and how to decompose them. Any help would be great.

Answer 1

Composite function means a function of a function.
If this makes it more confusing, then look at the following example:
h(x) = sin (x^2)
this function is made of 2 functions, sine function and square function.
so if we want to decompose, we can write let f(x)=sin x, g(x)=x^2.
to get f(g(x)), replace all 'x' in f(x) by g(x) and tell me what u get...

Answer 2

so f(x)=sin x^2?

Answer 3

f(x) is sin x, g(x) is x^2
so when u replace x in f(x) by g(x)=x^2
u get
f(g(x)) = sin x^2 = h(x)
did u get this ?
if yes, then try g(f(x))

Answer 4

wouldn't it be the same thing?

Answer 5

nopes, try to put 'x' in g(x) by f(x)=sin x, what do u get ?

Answer 6

(sin x)^2?

Answer 7

yes! thats correct.
so are (sinx)^2 and sin (x^2) same ?

Answer 8

no cause in (sinx)^2 you'd multiply sin and x first then ^2. in sin(x^2) you'd do ^2 first then sin.

Answer 9

that is correct, but do u know what a sine function is ?

Answer 10

not a flippin clue :)

Answer 11

Right now we're just doing regular functions i guess?
If you can even use the word regular in math...

Answer 12

no problem, try another one:
f(x) = x+1, g(x) = x^3
find, f(g(x)) and g(f(x))
and tell me what u get.

Answer 13

Alright. f(g(x))=x^3+1

g(f(x))=(x+1)^2

Answer 14

did u mistype g(f(x)) ?
it should be ^3 , isn't it ?

Answer 15

OH yeah I just had a brain fart :)

Answer 16

then you are correct.
now can u find f(g(x)) and g(f(x)) for any functions ?

Answer 17

I think so, its clearer now. Thank you oodles! :)

Answer 18

your welcome :)
want another example ?

Answer 19

No thanks i think i'm good. :) thanks