0. Functions

More composite functions Let ƒ(x) = | x | , g(x)= x² - 4 , F(x) = √x , G(x) = (1)/(x-2) Determine the following composite functions and give their domains.

G o g o ƒ

More composite functions Let ƒ(x) = | x | , g(x)= x² - 4 , F(x) = √x , G(x) = (1)/(x-2) Determine the following composite functions and give their domains.

G o G

Missing piece Let g(x) = x² + 3 Find a function ƒ  that produces the given composition.

(ƒ o g) (x) = x⁴ + 6x² + 9

Missing piece Let g(x) = x² + 3 Find a function ƒ  that produces the given composition.

(g o ƒ ) (x) = x⁴ + 3

Missing piece Let g(x) = x² + 3 Find a function ƒ that produces the given composition.

(g o ƒ ) (x) = x²⸍³ + 3

Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g  in the figure to determine the following function values. <IMAGE>

a. ƒ(g(-2))

Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g  in the figure to determine the following function values. <IMAGE>

e. g(g(-7))

Composition of even and odd functions from tables Assume ƒ is an even function, g is an odd function, and both are defined at 0. Use the (incomplete) table to evaluate the given compositions. <IMAGE>

a. ƒ(g(-1))

Composition of even and odd functions from tables Assume ƒ is an even function, g is an odd function, and both are defined at 0. Use the (incomplete) table to evaluate the given compositions. <IMAGE>

c. ƒ(g(-3))

Composition of even and odd functions from tables Assume ƒ is an even function, g is an odd function, and both are defined at 0. Use the (incomplete) table to evaluate the given compositions. <IMAGE>

e. g(g(-1))

Composition of even and odd functions from tables Assume ƒ is an even function, g is an odd function, and both are defined at 0. Use the (incomplete) table to evaluate the given compositions. <IMAGE>

g. ƒ (g(g(-2)))

Composition of even and odd functions from tables Assume ƒ is an even function, g is an odd function, and both are defined at 0. Use the (incomplete) table to evaluate the given compositions. <IMAGE>

i. g(g(g(-1)))

Composition of polynomials

Let ƒ be an nth-degree polynomial and let g be an mth-degree polynomial.

What is the degree of the following polynomials?

ƒ ⋅ f

Composition of polynomials

Let ƒ be an nth-degree polynomial and let g be an mth-degree polynomial.

What is the degree of the following polynomials?

ƒ o g

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Find h (ƒ (x)).