question_answer 71)

Let A = {?1, 0, 1, 2}, B = {?4, ?2, 0, 2} and f, g  : A  B be functions defined by f(x) = x2 ? x, and g(x) = 1,  Are f and g equal ? Justify your answer.       (Hint : One may note that two functions f : A  B and g : A  B such that f(a) = g (a)  are called equal functions.  

Answer:

Given f : A  B and g : A  B defined       As f(x) = x2 ? x and g(x) = 2       f(?1) = (?1)2 ? (?1) = 2; g(?1)                    Here f(0) = 02 ? 0 = 0; g(0)                            = 1 ? 1 = 0        f(2) = 22 ? 2 ; g(2) = 2             Clearly f(?1) = g(?1); f(0) = g(0); f(1) = g(1) and g(2) =g(2).       .