1. 1.5 Algebra of Functions

2. Given 2 functions f and g, we can put them together and make new functions
Sum (f + g)(x) = f (x) + g(x)
Difference (f – g)(x) = f (x) – g(x)
Product (f •g)(x) = f (x) • g(x)
Quotient
Domain of the combo function is those values each have in common

3. Ex 1) Find the new function and state the domain
f + g
f – g
f •g d)
= (f + g)(x)
= f (x) + g(x)
D = {x: x ≥ 1}
= (f – g)(x)
= f (x) – g(x)
D = {x: x ≥ 1}
= (f •g)(x)
= f (x) • g(x)
D = {x: x ≥ 1}
D = {x: x > 1}

4. We can combine functions in real world situations too
We can combine functions in real world situations too! Ex 2) The efficiency of an engine with a given heat output, in calories, can be calculated by finding the ratio of two fncts of heat input, D and N, where D(I) = I – 5700 & N(I) = I. a) Write a function for the efficiency of the engine in terms of heat output. b) Find efficiency when heat input is 17,200 cal

5. Another way to combine functions is called a composition of functions.
Given two functions f and g, the composite function, f ◦ g is (read f of g of x)
Domain is the set of elements of g such that g(x) is in domain of f
*Domains of f ◦ g and g ◦ f are not necessarily the same
(work from the inside out)

6. Ex 3)
Find composition and state domain of each a) b)
D = {x: x ≠ 0}

7. We can even “decompose” a function into two functions Ex 4) Determine two functions f and g such that
Can you see a function inside another function?
inside, this is g
so then

8. Homework
#105 Pg 36 #1-11 odd, 8, 13, 15, 23, 27, 29, 31, 33, 34, 37, 41