0. Functions

Composition of Functions

Copy and complete the following table.

a. <IMAGE>

Composition of Functions

Evaluate each expression using the functions

f(x) = 2 − x, g(x) = { −x, −2 ≤ x < 0

x − 1, 0 ≤ x ≤ 2

c. g(g(−1))

Combining Functions

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line (−∞,∞). Which of the following (where defined) are even? odd?

g. g ∘ f

Combining Functions

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line (−∞,∞). Which of the following (where defined) are even? odd?

d. f² = ff

Combining Functions

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line (−∞,∞). Which of the following (where defined) are even? odd?

b. f/g

Composition of Functions

Evaluate each expression using the functions

f(x) = 2 − x, g(x) = { −x, −2 ≤ x < 0

x − 1, 0 ≤ x ≤ 2

f. f(g(1/2))

Composition of Functions

Evaluate each expression using the functions

f(x) = 2 − x, g(x) = { −x, −2 ≤ x < 0

x − 1, 0 ≤ x ≤ 2

e. g(f(0))