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.
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
2 answers
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.
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.
3 answers