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Discuss the continuity of the function f where f is defined by 2x if x<0, 0 if 0<=x<=1, 4x if x>1

Q 15)
f(x)\left\{\begin{matrix} 2x & if &x<0 \\ 0& if &0\leq x\leq 1 \\ 4x&if & x>1 \end{matrix}\right.

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Given function is

Given function is satisfies for the all real values of x
case (i)  k < 0


Hence, function is continuous for all values of x < 0

case (ii)  x = 0

L.H.L at x= 0

R.H.L. at x = 0

L.H.L. = R.H.L. = f(0)
Hence, function is continuous at x = 0

case (iii)  k > 0


Hence , function is continuous for all values of x > 0

case (iv) k < 1


 Hence , function is continuous for all values of x < 1

case (v)  k > 1


 Hence , function is continuous for all values of x > 1

case (vi)  x = 1



Hence, function is not continuous at x = 1

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