If a function f ( x ) defined by f(x)= array c a x^2+b x+c, x -1 2 x^2+4 x+1,-1 < x < 1 c x^2+b x+a, x 1 array . is continuous on R , and _ x 3 2 f(x)=14 , then _ x -2 f(x)= x 3 2

Step-by-step solution

_ x 3 2 f(x)=14 C. 9 4 + 3 b 2 +a=14 9 c+6 b+4 a=56 ...(i) Right hand limit at x=-1=f(-1) aligned & _ x -1⁺ f(x)=a(-1)^2+b(-1)+c & 2(-1)^2+4(-1)+1= a - b + c aligned a-b+c=-1 ...(ii) Left hand limit at x=1=f(1) aligned & _ x 1⁻ f(x)=c+b+a & 2(1)^2+4(1)+1=a+b+c aligned a+b+c=7 ...(iii) [OBJEFrom equation (ii) & (iii): a+c=3 c=3-a From equation (iii): b+3=7 b=4 Now from (i): 9(3-a)+6 4+4 a=56 a=-1 and c =3-(1)=4 Now, _ x -2 f(x)=4 a-2 b+c=4 (-1)-2 4+4=-8