Question

Examine the following functions for continuity :

f(x) = | x – 5 |

Solution

Here f(x) = | x – 5 |
Function f is defined for all real numbers.
Let c be any real number.
$therefore space straight f left parenthesis straight c right parenthesis equals open vertical bar straight c minus 5 close vertical bar Also space Lt with straight x rightwards arrow straight c below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow straight c below open vertical bar straight x minus 5 close vertical bar equals open vertical bar straight c minus 5 close vertical bar therefore space Lt with straight x rightwards arrow straight c below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis straight c right parenthesis$
∴ f is continuous at.x = c.
But c is any real number
∴ f is continuous at every real number.

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Continuity And Differentiability

Examine the following functions for continuity :

f(x) = | x – 5 |

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For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

Examine the following functions for continuity : f(x) = | x – 5 |

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Examine the following functions for continuity :

f(x) = | x – 5 |