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Combination of Functions
Transcript of Combination of Functions
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)
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!
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.
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
Step 1: Evaluate j(7) ÷ p(4)
Step 2: (7) = 35 p(4) =5
j(7) ÷ p(4) 35 ÷ 5
Answer is= 7