Continuity And Differentiability

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.
∴ f(c) = c – 5
$Also space Lt with straight x rightwards arrow straight c below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow straight c below left parenthesis straight x minus 5 right parenthesis equals straight c minus 5 therefore space Lt with straight x rightwards arrow straight c below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis straight c right parenthesis$
∴ 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