Let f(x) = [x] + |1 – x|, – 1 ≤ x ≤ 3 and [x] is the largest integer not exceeding x. The number of points in [–1, 3] where f is not continuous is

Let f : [0, π] → R be defined byf (x) =(0 if x = 0,x sin 1x − 1x cos 1x if x̸ = 0.Is f continuous?

Let f(x) = [x] + |1 – x|, – 1 ≤ x ≤ 3 and [x] is the largest integer not exceeding x. The number of points in [–1, 3] where f is not continuous is

Let f(x)=∣∣2x2+5∣∣x|−3|,x∈R. If m and n denote the number of points where f is not continuous and not differentiable respectively, then m+n is equal to :

Let f, g : R → R be given functions. Suppose that f and g are continuous at c ∈ R.Prove that the functionl(x) := inf{f (x), g(x)}, x ∈ R,is continuous at c.

What is the largest negative integer value of x, for which ∣∣​ x 3 −1 ∣∣​ ≥2−x?Enter Answer: