jmc

Question

A function f has domain [0,2] and range [0,1]. (The notation [a,b] denotes x:a x b .) Let g(x) = 1 - f(x + 1).Then the domain of g(x) is [a,b], and the range of g(x) is [c,d]. Enter the ordered quadruple (a,b,c,d).

Accepted Answer

For g(x) = 1 - f(x + 1) to be defined, we need 0 x + 1 2,or -1 x 1. As y ranges over 0 y 1, 1 - y ranges from 1 to 0. Hence, (a,b,c,d) = (-1,1,0,1).