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Domain + Range of Transformation

Source: AMC 12 2008A Problem 12

February 17, 2008
algebrafunctiondomainAMC

Problem Statement

A function f f has domain [0,2] [0,2] and range [0,1] [0,1]. (The notation [a,b] [a,b] denotes {x:a≤x≤b} \{x: a\le x\le b\}.) What are the domain and range, respectively, of the function g g defined by g(x)\equal{}1\minus{}f(x\plus{}1)? (A)\ [\minus{}1,1],[\minus{}1,0] \qquad (B)\ [\minus{}1,1],[0,1] \qquad (C)\ [0,2],[\minus{}1,0] \qquad (D)\ [1,3],[\minus{}1,0] \qquad (E)\ [1,3],[0,1]
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