To prove whether f(x) is continuous at x = 0 & 1

If f(x) to be continuous at x = 0,we have to show that f(0)^–=f(0) ⁺ = f(0)

LHL = f(0)^– =

⇒ |(–0)| + |(–0)–1|

∴–|x| = |x| = x

⇒ |–1|

⇒ 1 ...(1)

RHL = f(0) ⁺ =

⇒ |0| + |0–1|

∴–|x| = |x| = x

⇒ |–1|

⇒ 1 ...(2)

From (1) & (2),we get f(0)^–=f(0) ⁺

Hence ,f(x) is continuous at x = 0

If f(x) to be continuous at x = 1,we have to show, f(1)^– =f(1) ⁺ = f(1)

LHL = f(1)^– ₌

⇒ |(1–0) + (–0)|

⇒ |(1)|

⇒ 1 ...(3)

RHL = f(1) ^{+ =}

⇒ |(1 + 0)| + |0|

∴–|x| = |x| = x

⇒ |1|

⇒ 1 ...(4)

From (3) & (4),we get f(1)^– ₌ f(1) ⁺

Hence ,f(x) is continuous at x = 1