English

The point of discountinuity of the function ,,f(x)={2x+3,x≤22x-3,x>2 is are -

Advertisements
Advertisements

Question

The point of discountinuity of the function `f(x) = {{:(2x + 3",", x ≤ 2),(2x - 3",", x > 2):}` is are

Options

  • 2

  • C < Z

  • C > Z

  • Not defined

MCQ

Solution

2

Explanation:

`f(x) = {{:(2x + 3",", x ≤ 2),(2x - 3",", x > 2):}`

At `x` = 2, L.H.L = `lim_(x -> 2) (2x + 3)` = 7

`f(2)` = 2 × 2 + 3 = 7

R.H.L = `lim_(x -> 2) + (2x - 3) = 2 xx 2 - 3` = 1

∴ `f` is discontinuous at `x` = 2

At `x = C < 2,  lim_(x -> 0) (2x + 3) = 2C + 3 = f(c)`

∴ `f` is continuous at `x` = C < 2

At `x = C > 2,  lim_(x -> 0) (2x - 3) = 2C - 3 = f(c)`

∴ `f` is continuous at `x` = C > 2

⇒ Point of discontinuty is `x` = 2.

shaalaa.com
  Is there an error in this question or solution?
Advertisements
Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×