If f(x) defined as given below, is continuous on R , then the value of a+b is equal to f(x)= array cc x, & x 0 x^2+a, & 0 3 array .

Step-by-step solution

f(x)= array cc x, & x 0 x^2+a, & 0 3 array . Given that, f(x) is continuous on R . Then, f(x) is continuous at n=0,3 f(0)= _ x 0⁺ f(x)= _ x 0⁻ f(x) Now, f(0)= 0=0 aligned & _ x 0⁺ f(x)= _ x 0⁺ (x^2+a )= _ h 0 (h^2+a )=a & _ x 0⁻ f(x)= _ x 0⁻ ( x)= _ h 0 (0-h)=0 & a=0 aligned Again, we must have f(3)= _ x 3⁺ f(x)= _ x 3⁻ f(x) Now, f(3)=b(3)+3=3 b+3 _ x 3⁺ f(x)=-3 3 b+3=-3 b=-2 Then, a+b=0-2=-2