Examine the following functions for continuity. f(x) = x - 5 - Vidyadip

Question

Examine the following functions for continuity.
f(x) = x - 5

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Answer

Here f(x) = x - 5Function f is defined for all real numbers.
Let c be any real number.
$\therefore$ f(c) = c - 5
Also $\ \ \ \text{Lt}\ \ \ \ \ \text{f(x)}\\ \text{x}\rightarrow{\text c}$ = $\ \ \ \text{Lt}\ \ \ \ \ \ \ (\text x - 5) = \text{c} - 5\\ \text{x}\rightarrow{\text c}$
$\therefore \text{Lt}\ \ \ \ \ \text{f(x)} = \text{f(c})\\ \ \ \text{x}\rightarrow{\text c}$
$\therefore$ f is continuous at x = c
But c is any real number.
$\therefore$ f is continuous at every real number.

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