f(x) = \(\begin{cases} 2x, if \; x < 0\\ 0, \;if\; 0\leq x\leq 1\\4x, \; if \;x > 1 \end{cases}\)

Question

Check the continuity

f(x) = (\begin{cases} 2x, if \; x < 0\ 0, \;if\; 0\leq x\leq 1\4x, \; if \;x > 1 \end{cases})

Answer 1

Case (i) : The domain of the function is R

f(1) = 0, LHL ≠ RHL hence discontinuous at x = 1

How ever the function is continuous

when a < 0, 0 < a < 1 and a > 1

Hence x = 1 is the only point of discontinuity.