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प्रश्न
Examine the following function for continuity:
f(x) = x – 5
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उत्तर
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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