Question

Find the functions and their domains. (Enter the domains in interval notation.) f(x) = x + 1/x, g(x) = (x + 17)/(x + 2) (a) f ? g (f ? g)(x) = (2x^2 + 38x + 293) / ((x + 2)(x + 17)) domain (-?, -17) ? (-17, -2) ? (-2, ?) (b) g ? f (g ? f)(x) = (x^2 + 17x + 1) / (x^2 + 2x + 1) domain (-?, -1) ? (-1, ?) (c) f ? f (f ? f)(x) = (x^4 + 3x^2 + 1) / (x(x^2 + 1)) domain (-?, 0) ? (0, ?) (d) g ? g (g ? g)(x) = (18x + 51) / (3x + 21) domain (-?, -7) ? (-7, ?)

          Find the functions and their domains. (Enter the domains in interval notation.)
f(x) = x + 1/x, g(x) = (x + 17)/(x + 2)

(a) f ? g
(f ? g)(x) = (2x^2 + 38x + 293) / ((x + 2)(x + 17))
domain (-?, -17) ? (-17, -2) ? (-2, ?)

(b) g ? f
(g ? f)(x) = (x^2 + 17x + 1) / (x^2 + 2x + 1)
domain (-?, -1) ? (-1, ?)

(c) f ? f
(f ? f)(x) = (x^4 + 3x^2 + 1) / (x(x^2 + 1))
domain (-?, 0) ? (0, ?)

(d) g ? g
(g ? g)(x) = (18x + 51) / (3x + 21)
domain (-?, -7) ? (-7, ?)

Find the functions and their domains. (Enter the domains in interval notation.)
f(x) = x + 1/x, g(x) = (x + 17)/(x + 2)

(a) f ? g
(f ? g)(x) = (2x^2 + 38x + 293) / ((x + 2)(x + 17))
domain (-?, -17) ? (-17, -2) ? (-2, ?)

(b) g ? f
(g ? f)(x) = (x^2 + 17x + 1) / (x^2 + 2x + 1)
domain (-?, -1) ? (-1, ?)

(c) f ? f
(f ? f)(x) = (x^4 + 3x^2 + 1) / (x(x^2 + 1))
domain (-?, 0) ? (0, ?)

(d) g ? g
(g ? g)(x) = (18x + 51) / (3x + 21)
domain (-?, -7) ? (-7, ?)

Added by Thomas K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

02/22/2023

Step 1

f(x) = x + 1 Domain of f(x): (-∞, ∞) g(x) = x + 17 Domain of g(x): (-∞, ∞) Now, let's find the compositions and their domains. (a) (f ∘ g)(x) = f(g(x)) = f(x + 17) = (x + 17) + 1 = x + 18 Domain of (f ∘ g)(x): (-∞, ∞) Show more…

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Find the functions and their domains. (Enter the domains in interval notation.) f(x) = x + 1/x, g(x) = (x + 17)/(x + 2) (a) f ∘ g (f ∘ g)(x) = (2x^2 + 38x + 293) / ((x + 2)(x + 17)) domain (-∐, -17) ∪ (-17, -2) ∪ (-2, ∐) (b) g ∘ f (g ∘ f)(x) = (x^2 + 17x + 1) / (x^2 + 2x + 1) domain (-∐, -1) ∪ (-1, ∐) (c) f ∘ f (f ∘ f)(x) = (x^4 + 3x^2 + 1) / (x(x^2 + 1)) domain (-∐, 0) ∪ (0, ∐) (d) g ∘ g (g ∘ g)(x) = (18x + 51) / (3x + 21) domain (-∐, -7) ∪ (-7, ∐)