Question

Find the points of discontinuity of the function f, where `f(x) = {{:(4x + 5",",  "if",  x ≤ 3),(4x - 5",",  "if",  x > 3):}`

Answer 1

`lim_(x -> 3) f(x) =  lim_(x -> 3^-) (4x + 5)`

= 4 × 3 + 5

`lim_(x -> 3) f(x)` = 17   .........(1)

`lim_(x -> 3) f(x) =  lim_(x -> 3^+) (4x - 5)`

= 4 × 3 – 5

`lim_(x -> 3) f(x)` = 12 – 5 = 7   .........(2)

From equations (1) and (2) we have

`lim_(x -> 3) f(x) ≠  lim_(x -> 3^+) f(x)`

∴ `lim_(x -> 3) f(x)` does not exist.

Hence f(x) is not continuous at x = 3.

∴ x = 3 is the point of dicontinuity.