Let f(x) is defined only for x ∈ (0, 5) and defined as f 2 (x) = 1 ∀ x ∈ (0, 5). Function f(x) is continuous for all x ∈ (0, 5) – {1, 2, 3, 4} (at x = 1, 2, 3, 4 f(x) may or may not be continuous). Find the number of possible function f(x) if it is discontinuous at
(i) One integral points in (0, 5)
(ii) two integral points in (0, 5)
(iii) three integral points in (0, 5)
(iv) four integral points in (0, 5)
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 24 (ii) 108 (iii) 216 (iv) 162
Sol. Number of ways of discontinuity at a point x = c are 3.
(i) LHL at x = c is equal to f(c) but not equal to RHL at x = c
(ii) LHL at x = c is not equal to f(c) but equal to RHL at x = c
(iii) LHL at x= c is neither equal to f(c) nor equal to RHL at x = c (where f(c)) is equal to RHL at x=c
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