JEE Advanced2020MathematicsContinuity and DifferentiabilityActual
Let the functions f : - 1 , 1 → ℝ and g : - 1 , 1 → - 1 , 1 be defined by f x = 2 x - 1 + 2 x + 1 & g x = x - x , where x denotes the greatest integer less than or equal to x . Let f ∘ g : - 1 , 1 → ℝ be the composite function defined by f ∘ g x = f g x . Suppose c is the number of points in the interval - 1 , 1 at which f ∘ g is not continuous, and suppose d is the
Correct answer
0
Step-by-step solution
f x = 2 x - 1 + 2 x + 1 = - 4 x , x - 1 2 2 , - 1 2 ≤ x ≤ 1 2 4 x , x > 1 2 g x = x f g x = - 4 g x , g x - 1 2 2 , - 1 2 ≤ g x ≤ 1 2 4 g x g x > 1 2 Graph of g x is f g x = 2 , x ∈ - 1 , - 1 2 ∪ 0 , 1 2 4 x + 1 x ∈ - 1 2 , 0 4 x x ∈ 1 2 , 1 c = 1 at x = 0 d = 3 at x = - 1 2 , 0 , 1 2 , ∴ c + d = 4 .