functions

posted by Johnathan

For each problem, construct two composite functions, . Evaluate each composite function for x=2

ok i have not dealt with composite functions can I please get some help with this as I have 20 questions to do can someone show me step by step on how to properly solve this equation is their a trick to doing this

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

1. Steve

how can you possibly have an assignment working with something you have not studied?

If you have f(x) and g(x) as functions, then there are two simple composite functions:

f(g(x)) and g(f(x))

Given your functions,
f(g) = g+1 = (x^2+2x+1)+1 x^2+2x+2
g(f) = f^2+2f+1
= (x+1)^2 + 2(x+1) + 1
= x^2+4x+4

Check the related problems below to see other worked examples. Wouldn't hurt to check your class text, either, so you will have "dealt" with them.

google will also turn up a wealth of examples.

2. Reiny

I will assume you defined you first function as
f(x) = x+1
also g(x) = x^2 + 2x + 1

the simple ones are where you do one of the arithmetic operations
e.g.
(f+g)(x) = (x+1) + (x^2 + 2x + 1)
= x^2 + 3x + 2

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

etc

the more complicated ones would be something like
f(g(x) )
= f(x^2+2x+1)
= (x^2+2x+1) + 1 = x^2 + 2x + 1

but

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

sometimes you will see this

(f o g)(x) , it is simply another way to write f(g(x))
notice that (g o f)(x) would be g(f(x) )

hope this will get you going.

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