Question

The point(s), at which the function f given by f(x) = `{("x"/|"x"|","  "x" < 0),(-1","  "x" ≥ 0):}` is continuous, is/are:

Options

• x ∈ R

• x = 0

• x ∈ R – {0}

• x = −1 and 1

Answer 1

x ∈ R

Explanation:

f(x) = `{("x"/"-x" = -1","  "x" < 0),(-1","  "x" ≥ 0):}`

f(x) = −1 ∀ x ∈ R

f(x) is continous ∀ x ∈ R as it is a constant function.