Please only help with parts D and E. Thank you 1. Let ƒ: R → R be a function, let function g: (-∞, 0) U (0, ∞) → R be defined by g(x) = 1, and let function h: [0, ∞) → R be defined byh(x)=√x.A. In terms of f(x), find an expression for the functions (gof)(x), (hof)(x), (gohof)(x), (hogof)(x).B. Henceforth, let P be the collection of all x for which f(x) is positive, let N be the collection of all x for which f(x) is negative, and let Z be thecollection of all x for which f(x) is zero. The natural domain of (g o ƒ) (x) is PU N. Explain.C. The natural domain of (h o ƒ) (x) is PU Z. Explain.D. The natural domain of (g ○ h o ƒ) (x) is P. Explain.E. The natural domain of (h o go ƒ) (x) is P. Explain.

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Answered: D. The natural domain of (go hof) (x)…

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D. The natural domain of (go hof) (x) is P. Explain. E. The natural domain of (ho gof)(x) is P. Explain.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 51E

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Question

Please only help with parts D and E. Thank you

1. Let ƒ: R → R be a function, let function g: (-∞, 0) U (0, ∞) → R be defined by g(x) = 1, and let function h: [0, ∞) → R be defined by
h(x)=√x.
A. In terms of f(x), find an expression for the functions (gof)(x), (hof)(x), (gohof)(x), (hogof)(x).
B. Henceforth, let P be the collection of all x for which f(x) is positive, let N be the collection of all x for which f(x) is negative, and let Z be the
collection of all x for which f(x) is zero. The natural domain of (g o ƒ) (x) is PU N. Explain.
C. The natural domain of (h o ƒ) (x) is PU Z. Explain.
D. The natural domain of (g ○ h o ƒ) (x) is P. Explain.
E. The natural domain of (h o go ƒ) (x) is P. Explain.

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