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

Answer 1

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