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
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
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.
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
(f+g)(x) = (x+1) + (x^2 + 2x + 1)
= x^2 + 3x + 2
similarly (g/f)(x) = (x^2+2x+1)/(x+1)
the more complicated ones would be something like
= (x^2+2x+1) + 1 = x^2 + 2x + 1
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.