Let A = {–1, 0, 1, 2}, B = {–4, –2, 0, 2} and f, g: A B be functions defined by f (x) = x2 – x, x A and , x A. 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) a A, are called equal functions).


It is given that A = {–1, 0, 1, 2}, B = {– 4, – 2, 0, 2}

And also, it is given that f, g: A B be functions defined by f (x) = x2 – x, x A and , x A


We can see that


f(-1) = (-1)2 – (-1) = 1 + 1 = 2



f(-1) = g(-1)


f(0) = (0)2 – 0 = 0 + 0 = 0



f(0) = g(0)


f(1) = (1)2 – 1 = 1- 1 = 0



f(1) = g(1)


f(2) = (2)2 – 2 = 4- 2 = 2



f(2) = g(2)


Thus, f(a) = g(a) . a ϵ A


Therefore, the functions f and g are equal.


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