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 .

Step-by-step solution

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 b3(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 .