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The sum f + g

xgxfxgf This just says that to find the sum of two functions, add them together. You should simplify by finding like terms.

1432 32 xxgxxf

1432 32 xxgf

424 23 xx

Combine like terms & put in descending

order

The difference f - g

xgxfxgf To find the difference between two functions, subtract the first from the second. CAUTION: Make sure you distribute the – to each term of the second function. You should simplify by combining like terms.

1432 32 xxgxxf

1432 32 xxgf

1432 32 xx

Distribute negative

224 23 xx

The product f • g

xgxfxgf To find the product of two functions, put parenthesis around them and multiply each term from the first function to each term of the second function.

1432 32 xxgxxf

1432 32 xxgf

31228 325 xxx

FOIL

Good idea to put in descending order but not required.

The quotient f /g

xgxf

xg

f

To find the quotient of two functions, put the first one over the second.

1432 32 xxgxxf

14

323

2

x

x

g

f Nothing more you could do here. (If you can reduce

these you should).

COMPOSITION

OFFUNCTIONS

“SUBSTITUTING ONE FUNCTION INTO ANOTHER”

The Composition Function

xgfxgf This is read “f composition g” and means to copy the f function down but where ever you see an x, substitute in the g function.

1432 32 xxgxxf

314223 xgf

51632321632 3636 xxxx

FOIL first and then distribute

the 2

xfgxfg This is read “g composition f” and means to copy the g function down but where ever you see an x, substitute in the f function.

1432 32 xxgxxf

132432 xfg

You could multiply this out but since it’s to the 3rd power we

won’t

xffxff This is read “f composition f” and means to copy the f function down but where ever you see an x, substitute in the f function. (So sub the function into itself).

1432 32 xxgxxf

332222 xff

You try:

11

xxgx

xf

gf

fg

You try:

5322 xxgxxxf

g

f

fg gfgf

gf gf