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Question
If the function f is continuous at x = I, then find f(1), where f(x) = `(x^2 - 3x + 2)/(x - 1),` for x ≠ 1
Solution
Consider ,
`lim_(x → 1) f(x) = lim_(x → 1)[(x^2 - 3x + 2)/(x - 1)]`
= `lim_(x → 1)[((x - 2)(x - 1))/((x - 1))]`
= `lim_(x → 1) (x - 2) ....[∵ x → 1 , x - 1 ≠ 0]`
= 1 - 2
= -1
Since f is continuous at x = 1.
∴ `lim_(x → 1) f(x) = f(1)`
⇒ ∴ f(1) = -1
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