If the function f x = a π - x + 1 ,     x ≤ 5 b x - π + 3 ,     x > 5 is continuous at x = 5 , then the value of a - b is:

Step-by-step solution

For continuity at x = 5 l i m x → 5 + f x = l i m x → 5 - f x = f 5 ⇒ l i m x → 5 + b x - π + 3 = l i m x → 5 - a π - x + 1 = a 5 - π + 1 We know that x =       x , x ≥ 0 - x , x < 0 ⇒ b 5 - π + 3 = a 5 - π + 1 = a 5 - π + 1 ⇒ b 5 - π + 3 = a 5 - π + 1 ⇒ 3 - 1 = a 5 - π - b 5 - π ⇒ a - b 5 - π = 2 ⇒ a - b = 2 5 - π .