1. Operations on Functions
Surgeons

2. For each of the following find and their domains.
Domain:
Domain:
Domain:
Domain:

3. For each of the following find and their domains.
Domain:
Domain:
Domain:
Domain:

4. For each of the following find and their domains.
Domain:
Domain:
Domain:
Domain:

5. Composition of functions:
If f and g are functions, then their composite f g is the
o
function with
[f g](x) = f[g(x)]
o
for each x in the domain of g such that g(x) is the
domain of f.
The function g is called the inner function, and its input is
x; f is the outer function and its input is g(x).

6. 1
If f(x) = 2x + 1 and g(x) = x
find [f g](x) and [g f](x)
o o
[f g](x)
o Domain:
Domain:
[g f](x)
o

7. EVEN FUNCTIONS
Graphically: A function is "even" if its graph is symmetrical about the y­axis.
These functions
are even...
These are
not ...
Symbolically (Algebraically)
a function is "even" IFF (if and only if) ƒ(­x) = ƒ(x)
Examples: Are these functions even?
1. f(x) = x² 2. g(x) = x² + 2x
f(­x) = (­x)² g(­x) = (­x)² + 2(­x)
f(­x) = x² g(­x) = x² ­ 2x
since f(­x)=f(x) since g(­x) is not equal to g(x)
f is an even function g is not an even function

8. ODD FUNCTIONS
Graphically: A function is "odd" if its graph is symmetrical about the origin.
These
functions
These are
are odd ... not ...
Symbolically (Algebraically)
a function is "odd" IFF (if and only if) ƒ(­x) = ­ƒ(x)
Examples: 1. ƒ(x) = x³ ­ x 2. g(x) = x³­ x²
ƒ(­x) = (­x)³ ­ (­x) g(­x) = (­x)³ ­ (­x)²
ƒ(x) = ­x³ + x g(x) = ­x³ ­ x²
­ƒ(x) = ­(x³ ­ x) ­g(x) = ­(x³­x²)
­ƒ(x) = ­x³ + x ­g(x) = ­x³+ x²
since ƒ(­x)= ­ƒ(x) since g(­x) is not equal to ­g(x)
ƒ is an odd function g is not an odd function

9. Exercise 1.9
Questions 1, 3, 5, 11, 15

10. Attachments
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