Question

`f(x) = {{:(x^3 - 3",", if x < 2),(x^2 + 1",", if x > 2):}` has how many point of discontinuity

Options

• 0

• 2

• 3

• 4

Answer 1

0

Explanation:

At `x` = 2, L.H.L

= `lim_(x -> 2) - (x^3 - 3) = 8 - 3` = 5

R.H.L = `lim_(x -> 2^+) = 4 + 1` = 5

`f(2) = 2^3 - 3 = 8 - 3` = 5

⇒ `f` is continuous at `x` = 2

At `x = C < 2, lim_(x -> C) (x^3 - 3) = C^3 - 3 = f(C)`

 At `x = C > 2, lim_(x -> C) (x^2 + 1) = C^2 + 1 = f(C)`

⇒ `f` is continuous for all x ∈ R

∴ There is no point of discontinuity.