Function f(x) is defined as follows f(x)= array cc a x-b, & x 1 3 x, & 1 x 2 b x^2-a, & x 2 array . If f(x) is continuous at x=1 , but discontinuous at x=2 then the locus of the point (a, b) is a straight line excluding the point where it c

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Function f(x) is defined as follows f(x)= array cc a x-b, & x 1 3 x, & 1 x 2 b x^2-a, & x 2 array . If f(x) is continuous at x=1 , but discontinuous at x=2 then the locus of the point (a, b) is a straight line excluding the point where it cuts the line

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Correct answer: A. y=3

Given; f(x) is continuous at x=1 aligned & f(1)= RHL & f(1)= _ x 1 +f(x) f(x)= _ h 0 f(1+h) aligned a-b= _ h 0 3(1+h) a-b=3 ...(i) Again, given f(x) is discontinuous at x=2 . aligned & LHL f(x) & _ x 2⁻ f(x) f(2) _ h 0 f(2-h) f(2) aligned _ h 0 3(2-h) 4 b-a 6 4 b-a ....(ii) Assume, 6=4 b-a then from (i) and (ii), we get b=3 locus y=3 Which is impossile ( 6 4 b-a) Hence, locus of (a, b) is x-y=3 excluding the point when it cuts the line y=3 .

Function f(x) is defined as follows f(x)= array cc a x-b, & x 1 3 x, & 1 x 2 b x^2-a, & x 2 array . If f(x) is continuous at x=1 , but discontinuous at x=2 then the locus of the point (a, b) is a straight line excluding the point where it cuts the line

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