Let g(x)= x² and f(x):=x+2 for XER, and let h be the composite function h:= go.f A) Find the direct image h (E) of E÷= {xER: 0≤x≤ 1} Answer gof→> (x + 2)² = x² + 4x+4 h(E) = {y: 4≤ y ≤9} B) Find the inverse image h (6) of 6:= {xt R: 0≤x≤ 4} If G:= {y:0 ≤ y ≤ 4}, theN Y = x² + 4x +4
Let g(x)= x² and f(x):=x+2 for XER, and let h be the composite function h:= go.f A) Find the direct image h (E) of E÷= {xER: 0≤x≤ 1} Answer gof→> (x + 2)² = x² + 4x+4 h(E) = {y: 4≤ y ≤9} B) Find the inverse image h (6) of 6:= {xt R: 0≤x≤ 4} If G:= {y:0 ≤ y ≤ 4}, theN Y = x² + 4x +4
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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Transcribed Image Text:2
Let g(x)= x
and f(x):=x+2 for XER, and let
h be the composite function h: = go f
A) Find the direct image h (E) of E÷= {xER: 0 ≤ x ≤ 1}
Answer
gof → (x + 2)² = x² + 4x +4
2
h(E) = {y: 4≤ y
≤9}
1
B) Find the inverse image h¨(6) of 6:= {XER: 0≤x≤ 4}
IF G:= {y: 0≤ y ≤43, then
If
2
y = x² + 4x + 4
=
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