Question

Find the points of discontinuity of the following point .

(1) f(x) = 1/2sinx-1

(2) f(x) = 1/x²-|3x|+2 ​

Answer 1

Hi !!

Solution:- (1)

f(x) = 1/2sinx-1

f(x) is discontinuous when 2sinx-1 =0

or , Sinx = 1/2 i.e x= 2nπ+π/6 or, x = 2nπ+5π/6 n belongs to z

Solution :- (2) f(x) = 1/x²-3|x|+2

f(x) is discontinuous when

x² -3|X| + 2 = 0

or, x²-3|x| + 2 = 0

or, (|x|-1) (|x|-2)= 0v

or , x = +-1. +-2

hence at +- 1 and +-2 it will be discontinues

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Hope it helps you !!

@Raj❤

Answer 2

Step-by-step explanation:

1.

Given,

f(x) = 1/2sinx - 1

=> 2 sinx - 1 = 0

=> sinx = 1/2

=> x = π/6

Therefore,

x = 2nπ + π/6

(2)

Given,

f(x) = 1/x² - |3x| + 2

=> x² - 3x + 2 = 0

For x < 0 :

x = -2 (or) x = - 1

For x ≥ 0:

x = 1 (or) x = 2

Thus,

x = ±1, ±2

Hope it helps!