Question

Question 6: Find all points of discontinuity of f, where f is defined by f(x) 2x+3, if x ≤ 2 2x-3, if x > 2

Class 12 - Math - Continuity and Differentiability

Answer 1

In the above attachment,
L.H.L. is equal to R.H.L but they both are unequal to f (2).

Therefore, f (x) is discontinuous at x =2.

Hope it helps...

Answer 2

The given function f(x) = {2x+3 if x≤2
2x-3 if x>2

When x<1 ,f(x) = x+2 which being polynomial is continuous for all x<1 
When x>1 f(x) = x-2 ,which being polynomial is continuous for all x>1 


Now we consider point x= 2
At x = 2 
L.H.L = lim x→2- f(x) = lim x→2- f(2x+3) 
= lim h→0 { 2(2-h) +3 }
= 7

Now R.H.L 
= lim x→2+ f(x) = lim x→2+ f(2x-3) 
= lim h→ 0 2(2-h) -3 
= 1 
Thus L.H.L ≠ R.H.L 
hence Function is discontinuous at x = 2