Question

Is the function defined by f(x) = | x |, a continuous function ?

Solution

f(x) = |x|.D_f=R
Let a be any real number ∈ D_{f
$Now space Lt with straight x rightwards arrow straight a below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow straight a below open vertical bar straight x close vertical bar equals open vertical bar straight a close vertical bar Also space straight f left parenthesis straight a right parenthesis equals open vertical bar straight a close vertical bar therefore space Lt with straight x rightwards arrow straight a below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis straight a right parenthesis space rightwards double arrow space straight f space is space continous space at space straight x equals 0$}But a is any real number ∈ D_f∴ f is continuous function
⇒ | x | is continuous at every point of domain.

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Continuity And Differentiability

Is the function defined by f(x) = | x |, a continuous function ?

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