 Hello and welcome to the session. Let us understand the following problem today. Let a is equal to minus 1, 0, 1, 2, b is equal to minus 4, minus 2, 0, 2 and f, g are that from a to b b function defined by fx is equal to x square minus x, x belongs to a and g of x is equal to 2 into mod of x minus 1 by 2 minus 1, x belongs to a. Are f and g equal justify your answer? We know that two functions are equal f from a to b and g from a to b are such that f of a is equal to 0 of a where all a belongs to a. Let a is equal to minus 1, 0, 1, 2 and b is equal to minus 4, minus 2, 0, 2, f be a function from a to b and g be a function from a to b defined by x is equal to x square minus x, g of x is equal to 2 into mod of x minus half minus 1 for all x belongs to a. Now we check whether f of a is equal to g of a for all x belongs to a, x is equal to minus 1, fx is equal to minus 1 the whole square plus minus 1 which is equal to 1 plus 1 which is equal to 2, g of x is equal to 2 into mod of minus 1 minus half minus 1 which is equal to 2 into mod of minus 3 by 2 minus 1 which is equal to 2 into 3 by 2 minus 1 which is equal to 3 minus 1 which is equal to 2 therefore minus 1 is equal to f of minus 1 now is equal to 0, f of 0 is equal to 0 square minus 0 which is equal to 0 and g of 0 is equal to 2 into mod of 0 minus half minus 1 which is equal to 2 into mod of minus half minus 1 which is equal to 2 into half minus 1 which is equal to 1 minus 1 which is equal to 0. Therefore f of 0 is equal to g of 0. Now at x is equal to 1, f of 1 is equal to 1 square minus 1 which is equal to 1 minus 1 which is equal to 0. And g of 1 is equal to 2 into 1 minus half minus 1 which is equal to 2 into mod of half minus 1 which is equal to 1 minus 1 which is equal to 0. Therefore f of 1 is also equal to g of 1. Now at x is equal to 2, f of 2 is equal to 2 square minus 2 which is equal to 4 minus 2 which is equal to 2 and g of 2 is equal to 2 into mod of 2 minus half minus 1 which is equal to 2 into mod of 3 by 2 minus 1 which is equal to 3 minus 1 which is equal to 2. Therefore f of 2 is also equal to g of 2. Thus for all a belongs to a, f of a is equal to g of a which implies f and g are equal functions. Therefore the required answer is yes. I hope you understood the problem bye and have a nice day.