 = 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).](https://image.slidesharecdn.com/compoffunctions0922-090922155802-phpapp02/85/Comp-Of-Functions-0922-5-320.jpg)
 and [g f](x)
o o
[f g](x)
o Domain:
Domain:
[g f](x)
o](https://image.slidesharecdn.com/compoffunctions0922-090922155802-phpapp02/85/Comp-Of-Functions-0922-6-320.jpg)
Comp Of Functions 0922
- 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
- 10. Attachments Surgeons