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
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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
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
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