If f(x)= array l m x+1, x 2 x+n, x> 2 array . is continuous at x= 2 , then

Step-by-step solution

For the function f(x) to be continuous at x = 2 , the left-hand limit, right-hand limit, and the value of the function at x = 2 must be equal. The left-hand limit is given by _ x 2 ⁻ f(x) = _ x 2 ⁻ (mx + 1) = m ( 2 ) + 1 . The value of the function at x = 2 is f ( 2 ) = m ( 2 ) + 1 . The right-hand limit is given by _ x 2 ⁺ f(x) = _ x 2 ⁺ ( x + n) = ( 2 ) + n = 1 + n . Equating the left-hand limit and the right-hand limit: m 2 + 1 = 1 + n Subtracting 1 from both sides: m 2 = n Solving for m : m = 2n . Answer: m= 2