If f(x) = {x} & g(x) = [x] (where {. } & [.] denotes the fractional part and the integral part functions respectively), then discuss the continuity of :
(i) h(x) = f(x). g(x) at x = 1 and 2
(ii) h(x) = f(x) + g(x) at x = 1
(iii) h(x) = f(x) – g(x) at x = 1
(iv) h(x) = g(x) + 
at x = 1 and 2
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)continuous at x = 1 (ii)continuous
(iii)discontinuous (iv)continuous at x = 1, 2
Sol. (i) h(x) = {x} [x]
at x = 1 h(1) = 0 LHL = 0 RHL = 0
at x = 2 h(2) = 0 LHL = 1 RHL = 0
(ii) h(x) = {x} + [x] = x at x = 1 continuous
(iii) h(x) = {x} – [x] = x – 2[x] discontinuous at x = 1
(iv) h(x) = 
+ [x]
at x = 1 h(1) = 1 LHL = 1 RHL = 1
at x = 2 h(2) = 2 LHL = 2 RHL = 2
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