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Question
Examine the following function for continuity:
f (x) = x – 5
Solution
Let a be a real number, then,
`lim_(x->a^+) f (x) = lim_(h->0) (a + h) - 5 = a - 5`
`lim_(x->a^-) f (x) = lim_(h->0) (a - h) -5 = a - 5`
Also f(a) = a - 5
∵ `lim_(x->a^+) f(x) = lim_(x->a^-) f(x)f(a)`
Hence, the given function f(x) = (x - 5) is continuous.
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