Question

1. The following are notations for composite functions EXCEPT,
a. (p(x))
b. f(x)g(x)
c. (s 0)(x)
d. f(g(x))​

Answer 1

Answer:

Composition of functions on a finite set: If f = {(1, 1), (2, 3), (3, 1), (4, 2)}, and g = {(1, 2), (2, 3), (3, 1), (4, 2)}, then g ∘ f = {(1, 2), (2, 1), (3, 2), (4, 3)}, as shown in the figure.

Composition of functions on an infinite set: If f: ℝ → ℝ (where ℝ is the set of all real numbers) is given by f(x) = 2x + 4 and g: ℝ → ℝ is given by g(x) = x3, then:

(f ∘ g)(x) = f(g(x)) = f(x3) = 2x3 + 4, and

(g ∘ f)(x) = g(f(x)) = g(2x + 4) = (2x + 4)3.

If an airplane's altitude at time t is a(t), and the air pressure at altitude x is p(x), then (p ∘ a)(t) is the pressure around the plane at time t.