If the function f(x), defined below, is continuous on the interval [0,8], then f(x)= \ array cc x^2+a x+b & , 0 x 2 \ 3 x+2, & 2 x 4 \ 2 a x+5 b, & 4 x 8 array .

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Correct answer: A. a=3, b=-2

Here, f(x) is continuous on the interval [0,8]. So it will also be continuous on 2 and 4. At x=2, _ x 2^ - f(x)= _ x 2^ + f(x) _ x 2^ - (x^2+ ax + b )= _ x 2^ + (3 x+2) 4+2 a+b=3(2)+2 2 a+b=4 ...(i) At x=4 _ x 4^ - f(x)= _ x 4^ + f(x) _ x 4^ - (3 x+2)= _ x 4^ + 2 a x+5 b 3(4)+2=2 a(4)+5 b 8 a+5 b=14 .......(ii) On solving Eqs. (i) and (ii), we get a=3 and b=-2.

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