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Sample Question 12:
A \(f\) 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 \(g(x)=1-f(x+1)\)?
\(\mathrm{(A)}\ [-1,1],[-1,0]\qquad\mathrm{(B)}\ [-1,1],[0,1]\qquad\textbf{(C)}\ [0,2],[-1,0]\qquad\mathrm{(D)}\ [1,3],[-1,0]\qquad\mathrm{(E)}\ [1,3],[0,1]\)