Let t denote the greatest integer ≤ t and t denote the fractional part of t . Then integral value of α for which the left hand limit of the function f x = 1 + x + α 2 x + x + x - 1 2 x + x at x = 0 is equal to α - 4 3 is _____

Step-by-step solution

Given, f x = 1 + x + α 2 x + x + x - 1 2 x + x lim x → 0 - f x = α - 4 3 lim x → 0 - 1 + x + α x + x + x + x - 1 2 x + x = α - 4 3 ⇒ 0 + α - 1 - 2 - 1 = α - 4 3 ⇒ 2 - 1 α = α - 4 3 ⇒ α + 1 α = 10 3 On solving above equation we get, ⇒ α = 3 ; α ∈ I