Combination of

Functions By: Tyler, Brittany

and Kaitlyn Composite Functions Given f (x) = 3x – 4 and g(x) = x2 + 6, find:

a. (f o g)(x) b. (g o f)(x)

Solution:

We begin the composition of f with g. Since (f o g)(x) = f (g(x)), replace each occurrence of x in the equation for f by g(x). Mr. P: You know you want to give us a 100% on this

project because we did such an awesome

amazing job on it!

Thanks

Brittany, Tyler, Kaitlyn The difference quotient for the function is: Read that book...

No never mind, it might kill me. Make sure to study for up-coming test!

Ehhh, maybe later! Sum of Functions Quotient of Functions Product of Functions Difference of Functions Example:

Find (F+G)(2) ?

Then you would substitute, or "plug in" 2 for every X in the function:

so say that f(x)=3x^2+2x,

f(2) would be 3(2)^2 + 2(2).

same in the sum of functions.

For example,

f(x)=3x^2+2x, and g(x)=4x^2+5x, then

(f+g)(2) would equal [3(2)^2+2(2)] + [4(2)^2+5(2)], and then you would evaluate. Difference of Functions Video . Example:

f(x) = 7x - 5

g(x) = x^3 + 4x

find (f * g)(x)

(f o g)(x) = f(x) * g(x)

(7x-5) * (x^3 + 4x)

(7x-5) * x^3 + (7x-5) * 4x

Answer = 7x^4 - 5x^3 + 28x^2 - 20x f (x) = 3x – 4 This is the given equation for f.

(f o g)(x) = f (g(x)) = 3g(x) – 4

= 3(x2 + 6) – 4 Replace g(x) with x2 + 6.

= 3x2 + 18 – 4 Use the distributive property.

= 3x2 + 14 Simplify

Thus, (f o g)(x) = 3x2 + 14 Example 1:

f(x) = 3x

g(x) = 5x+2

What is f(8) ÷ g(2) ?

Step 1: evaluate the individual functions

f(8) = 3 × 8 = 24

g(2) = 5 ×2 +2 = 12

Step 2: Divide the values that your functions produced

f(8) ÷ g(2) = 24 ÷ 12

Answer is= 2 Example 2:

j(x) = 5x

p(x) =x+1

Step 1: Evaluate j(7) ÷ p(4)

Step 2: (7) = 35 p(4) =5

j(7) ÷ p(4) 35 ÷ 5

Answer is= 7

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# Combination of Functions

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