Project Help Notebook by Keith Stroyan

Help NoteBook Copyright 1998 by Academic Press, Inc. - All rights reserved.
Modify this Notebook to prepare your project report.

Project 10: Functional Identities

by A. Student and B. Pupil

with technical help from Da LabMonitor and Help Notebook

My Project Introduction

Write this last.  Begin with the basic question and state your main finding clearly, but with few technical details.  You might even modify the title of this section to make it more interesting.

Beginning Explorations or Computer Experiments

Section 1

This project is intended to be mostly paper and pencil math.  However, you can use Mathematica's BasicTypesetting Palette to type your results..

The following computations might help get you started.  Break them up (using Divide Cell) if you wish.

\(Clear[f, x, y, m, b]; 
f[x_]\  = m\ x\  + \ b\)f[x]  +  f[y]f[x + y]f[x]*f[y]\(x\  = \ 2; 
y\  = \ 3; 
f[x]\  + \ f[y]\)f[x + y]f[x]*f[y]Expand[f[x]*f[y]]\(b = 0; 
Clear[x, y]; 
f[x]\  + \ f[y]\)f[x + y]f[x]*f[y]\(x\  = \ 2; 
y\  = \ 3; 
f[x]\  + \ f[y]\)Expand[f[x]  +  f[y]]f[x + y]f[x]*f[y]Expand[f[x]*f[y]]

\(Clear[f, x, y]; 
f[x_]\  = 2\^x\)f[x]  +  f[y]f[x + y]f[x]*f[y]\(x\  = \ 2; 
y\  = \ 3; 
f[x]\  + \ f[y]\)f[x + y]f[x]*f[y]

\(Clear[f, g, x, y]; 
f[x_]\  = \ Cos[x]\)g[x_]  =  Sin[x]f[x + y]f[x] f[y] - g[x] g[y]Simplify[f[x] f[y] - g[x] g[y]]f[x] + f[y]g[x + y]g[x] f[y] + f[x] g[y]Simplify[g[x] f[y] + f[x] g[y]]g[x] + g[y]

\(Clear[f, g, x, y]; 
f[x_]\  = \ 1/x\)g[x_]  =  (Sqrt[x])f[x + y]f[x] f[y] - g[x] g[y]Simplify[f[x] f[y] - g[x] g[y]]f[x] + f[y]g[x + y]g[x] f[y] + f[x] g[y]Simplify[g[x] f[y] + f[x] g[y]]g[x] + g[y]