Question

Let f be the function defined by

f(x) = `{{:((x^2 - 1)/(x^2 - 2|x - 1| - 1)",", x ≠ 1),(1/2",", x = 1):}`

विकल्प

• The function is continuous for all values of x

• The function is continuous only for x > 1

• The function is continuous at x = 1

• The function is not continuous at x = 1

Answer 1

The function is not continuous at x = 1

Explanation:

For x < 1, f(x) = `(x^2 - 1)/(x^2 + 2x - 3) = (x + 1)/(x + 3)`

∴ `lim_(x rightarrow 1^-)` f(x) = `1/2`

For x > 1, f(x) = `(x^2 - 1)/(x^2 - 2x + 1) = (x + 1)/(x - 1)` 

∴ `lim_(x rightarrow 1^+)` f(x) = ∞

∴ The function is not continuous at x = 1.