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Solution If f(x) = Vx and g(x) = V5 - x, find each function and its domain. (Enter your answers using interval notation, when necessary.) (a) fog (b) g of (c) fof (d) gog (a) (fo g)(x) = f(g(x)) = F( 8(x) = V V5 -x (-x,5] The domain of fogis {x|5 – x 2 0} = {xIx s which is the interval (b) (g o f)(x) = g(f(x)) = g For Vx to be defined we must have x 2 For V 5 - Vx to be defined, we must have 5 - Vx 2 0 that is Vxs 5, or x s| |. Thus we have so the domain of gofis the closed interval (c) (fo f)(x) = f(f(x)) = The domain of fo fis the interval

Solution If f(x) = Vx and g(x) = V5 - x, find each function and its domain. (Enter your answers using interval notation, when necessary.) (a) fog (b) g of (c) fof (d) gog (a) (fo g)(x) = f(g(x)) = F( 8(x) = V V5 -x (-x,5] The domain of fogis {x|5 – x 2 0} = {xIx s which is the interval (b) (g o f)(x) = g(f(x)) = g For Vx to be defined we must have x 2 For V 5 - Vx to be defined, we must have 5 - Vx 2 0 that is Vxs 5, or x s| |. Thus we have so the domain of gofis the closed interval (c) (fo f)(x) = f(f(x)) = The domain of fo fis the interval

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solution If f(x) = Vx and g(x) = V5 - x, find each function and its domain. (Enter your answers using interval notation, when necessary.) (a) fog (b) g of (c) fof (d) gog (a) (fo g)(x) = f(g(x)) = F( 8(x) = V V5 -x (-x,5] The domain of fogis {x|5 – x 2 0} = {xIx s which is the interval (b) (g o f)(x) = g(f(x)) = g For Vx to be defined we must have x 2 For V 5 - Vx to be defined, we must have 5 - Vx 2 0 that is Vxs 5, or x s| |. Thus we have so the domain of gofis the closed interval (c) (fo f)(x) = f(f(x)) = The domain of fo fis the interval
Transcribed Image Text:Solution If f(x) = Vx and g(x) = V5 - x, find each function and its domain. (Enter your answers using interval notation, when necessary.) (a) fog (b) g of (c) fof (d) gog (a) (fo g)(x) = f(g(x)) = F( 8(x) = V V5 -x (-x,5] The domain of fogis {x|5 – x 2 0} = {xIx s which is the interval (b) (g o f)(x) = g(f(x)) = g For Vx to be defined we must have x 2 For V 5 - Vx to be defined, we must have 5 - Vx 2 0 that is Vxs 5, or x s| |. Thus we have so the domain of gofis the closed interval (c) (fo f)(x) = f(f(x)) = The domain of fo fis the interval
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