# composite functions with sine

• Feb 12th 2010, 07:43 PM
snypeshow
composite functions with sine
f(x) = sin (x)
g(x) = x^2 - x + 1

the question basically asks for a composite g o f, or g(f(x)). I get:

= sin (x^2 - x + 1)
= sin^2x - sin x + .... (i dont know how to multiply sin with 1, is it just sin(1) ?)

its kinda confusing for me, since sine isn't really a variable, it's more like a "modifier" for a variable
• Feb 12th 2010, 08:19 PM
TKHunny
Quote:

Originally Posted by snypeshow
= sin (x^2 - x + 1)

This is f(g(x)). You want g(f(x)).

Quote:

= sin^2x - sin x + .... (i dont know how to multiply sin with 1, is it just sin(1) ?)
No, no, no and no. Never, EVER do that again. sin(x) is a function. It is not a modifier. Never, ever, split up its argument like that. Ever. "sin" means nothing - except in a religious sense. "sin" must have an argument.

Didn't we do g(f(x)) already in the Domain and Range question?
• Feb 12th 2010, 09:31 PM
snypeshow
Quote:

Originally Posted by TKHunny

Didn't we do g(f(x)) already in the Domain and Range question?

the domain and range question was multiplying 2 functions. this question is about composite functions.

Composite functions are when you have 2 functions (so f(x) and g(x)) and f o g means that g(x) replaces x in the function f(x)

so in the question, f(x) = sin x and g(x) = x^2 - x + 1
I'm looking for f(g(x)) (sorry, i said the opposite in my first post, my fault)

so f(g(x)) = sin (x^2 - x + 1)

how would i evaluate f(g(x))? or do i leave it as is?

(and yeah i guess im not too good with trig, as you could probably tell :D)
• Feb 13th 2010, 10:29 AM
TKHunny
No worries. Just pin down what the notation means.

Quote:

Originally Posted by snypeshow
so f(g(x)) = sin (x^2 - x + 1)

Good.

Quote:

How would i evaluate f(g(x))? or do i leave it as is?
There is some push to "simplify". "Evaluate" really doesn't mean much.
• Feb 13th 2010, 01:38 PM
snypeshow
Quote:

Originally Posted by TKHunny
No worries. Just pin down what the notation means.

Good.

There is some push to "simplify". "Evaluate" really doesn't mean much.

so f(g(x)) = sin (x^2 - x + 1) can't be broken down any more right?
• Feb 18th 2010, 10:43 AM
snypeshow
bump

and how would i find the domain and range for this question?
• Feb 18th 2010, 11:08 AM
icemanfan
Quote:

Originally Posted by snypeshow
so f(g(x)) = sin (x^2 - x + 1) can't be broken down any more right?

Using the trig identity

$\displaystyle \sin(a + b) = \sin a \cos b + \cos a \sin b$

you have

$\displaystyle \sin (x^2 - x + 1) = \sin ((x^2 - x) + 1) =$

$\displaystyle \sin (x^2 - x) \cos 1 + \cos(x^2 - x) \sin 1$

and you can break that down even further using

$\displaystyle \sin(a - b) = \sin a \cos b - \cos a \sin b$ and

$\displaystyle \cos(a - b) = \cos a \cos b + \sin a \sin b$
• Feb 18th 2010, 11:17 AM
snypeshow
thanks!

I'm also looking for the domain and range for this function (specifically the range)
• Feb 18th 2010, 11:24 AM
icemanfan
Quote:

Originally Posted by snypeshow
thanks!

I'm also looking for the domain and range for this function (specifically the range)

What is the range of the sine function?