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Question
Examine whether the function is continuous at the points indicated against them:
f(x) `{:(= x^3 - 2x + 1",", "if" x ≤ 2),(= 3x - 2",", "if" x > 2):}}` at x = 2
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Solution
`lim_(x -> 2^-) "f"(x) = lim_(x -> 2^-) (x^3 - 2x + 1)`
= (2)3 – 2(2) + 1
= 5
`lim_(x -> 2^+) "f"(x) = lim_(x -> 2^+) (3x - 2)`
= 3(2) – 2
= 4
∴ `lim_(x -> 2^-) "f"(x) ≠ lim_(x -> 2^+) "f"(x)`
∴ f(x) is discontinuous at x = 2
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