# Composition of functions

• September 22nd 2010, 01:43 PM
spoc21
Composition of functions
Hi, I'm having a bit of trouble with the following question:
Given the following, find:

f = $10 sin (11x)$

g = $(11-x)/(1+x)$

Find (g o f)

I'm really confused with this problem, and have attempted it numerous times. I would greatly appreciate any help
• September 22nd 2010, 01:49 PM
Traveller
Interpret it as f(x) = 10sin(11x) and g(x) = (11 - y )/(1 + y ) where y = f(x).
• September 22nd 2010, 03:42 PM
Soroban
Hello, spoc21!

Do you know what a composite function is?

Quote:

$\text{Given: }\;\begin{Bmatrix}f(x) &=& 10\sin11x \\ \\[-3mm]
g(x) &=& \dfrac{11-x}{1+x} \end{Bmatrix}$

$\text{Find }\,(g\,\circ\, f)$

We have: . $g\,\circ\,f \;=\;g(f(x)) \;=\;g\left(10\sin11x\right) \;=\; \dfrac{11 - 10\sin11x}{1 + 10\sin11x}$