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Q 15) Find the points of discontinuity, if any, of the following functions:
$f(x)\left\{\begin{matrix} 2x & if &x<0 \\ 0& if &0\leq x\leq 1 \\ 4x&if & x>1 \end{matrix}\right.$

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Given function is

Given function is satisfied for all real values of x

case (i) k < 0

Hence, the 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, the function is continuous at x = 0

case (iii) k > 0

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

case (iv) k < 1

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

case (v) k > 1

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

case (vi) x = 1

Hence, the function is not continuous at x = 1

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Gautam harsolia

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