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Misc 1 The relation f is defined by f (x) = {█("x2 , 0" ≤"x" ≤"3 " @"3x, 3" ≤"x" ≤"10" )┤ The relation g is defined by g (x) = {█("x2 , 0" ≤"x" ≤"2 " @"3x, 2" ≤"x" ≤"10" )┤ Show that f is a function and g is not a function. A relation is a function if Every element of first set has an image Every element of first set has only one image Finding value of f(x) and g(x) for different values of x For f(x) f (x) = {█("x2 , 0" ≤"x" ≤"3 " @"3x, 3" ≤"x" ≤"10" )┤ Therefore, for 0 ≤ x ≤ 10, there is unique f(x), Hence, it has unique image Thus, f(x) is a function For g(x) g (x) = {█("x2 , 0" ≤"x" ≤"2 " @"3x, 2" ≤"x" ≤"10" )┤ For x = 2, g(x) = 4 & 6 Thus, Element 2 corresponds “ to two different images 4 & 6. Hence, relation g(x) is not a function.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.