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प्रश्न
Find the points of discontinuity of the function f, where `f(x) = {{:(4x + 5",", "if", x ≤ 3),(4x - 5",", "if", x > 3):}`
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उत्तर
`lim_(x -> 3) f(x) = lim_(x -> 3^-) (4x + 5)`
= 4 × 3 + 5
`lim_(x -> 3) f(x)` = 17 .........(1)
`lim_(x -> 3) f(x) = lim_(x -> 3^+) (4x - 5)`
= 4 × 3 – 5
`lim_(x -> 3) f(x)` = 12 – 5 = 7 .........(2)
From equations (1) and (2) we have
`lim_(x -> 3) f(x) ≠ lim_(x -> 3^+) f(x)`
∴ `lim_(x -> 3) f(x)` does not exist.
Hence f(x) is not continuous at x = 3.
∴ x = 3 is the point of dicontinuity.
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