2008 AMC12 A #12

A function $f$ has domain $[0, \; 2]$ and range $[0, \; 1]$. (The notation $[a, \; b]$ denotes $\{ x\; : \; a \le x \le b \}$.) What are the domain and range, respectively, of the function $g$ defined by $g(x)=1-f(1+x)$ ?

(A) $[-1, \; 1 ], \; [-1, \; 0]$

(B) $[-1, \; 1 ], \; [0, \; 1]$

(C) $[0, \; 2 ], \; [-1, \; 0]$

(D) $[1, \; 3 ], \; [-1, \; 0]$

(E) $[1, \; 3], \; [0, \; 1]$

정답 (B)