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

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.

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.

Sure! I'd be happy to help you with composite functions.

To find composite functions, you will need to combine two functions by performing the operation of one function on the input of the other function.

Let's start by constructing the first composite function using f(x) = x + 1 and g(x) = x^2 + 2x + 1.

1. First, substitute g(x) into f(x). We will replace x in f(x) with g(x):
f(g(x)) = f(x^2 + 2x + 1)

2. Now, substitute x = 2 into the composite function f(g(x)):
f(g(2)) = f(2^2 + 2(2) + 1)

3. Simplify the expression within parentheses in the composite function:
f(g(2)) = f(4 + 4 + 1)
= f(9)

4. Finally, substitute the value x = 9 into f(x):
f(g(2)) = 9 + 1
= 10

Therefore, the value of the composite function f(g(x)) when x = 2 is 10.

Now, let's construct the second composite function using the same functions:

1. Substitute f(x) into g(x). We will replace x in g(x) with f(x):
g(f(x)) = g(x + 1)

2. Substitute x = 2 into the composite function g(f(x)):
g(f(2)) = g(2 + 1)

3. Simplify the expression within parentheses in the composite function:
g(f(2)) = g(3)

4. Finally, substitute the value x = 3 into g(x):
g(f(2)) = 3^2 + 2(3) + 1
= 9 + 6 + 1
= 16

Therefore, the value of the composite function g(f(x)) when x = 2 is 16.

To solve each composite function, follow these steps:
1. Substitute the given x-value into the innermost function.
2. Perform the necessary operations to simplify the expression.
3. Substitute this simplified expression into the outer function.
4. Perform the necessary operations to simplify the composite function further, if possible.

Repeat these steps for each composite function you need to evaluate.