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

Question

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

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Answer

The given function is f(x) = x - 5
We know that f is defined at every real number k and its value at k is k - 5.
We can see that $\mathop {\lim }\limits_{x \to {\mathbf{k}}} f(x) = \mathop {\lim }\limits_{x \to k} (x - 5) = k - 5 = f(k)$
Thus, $\mathop {\lim }\limits_{{{x}} \to {{k}}} {{f}}({{x}}) = {{f}}({{k}})$
Therefore, f is continuous at every real number and thus, it is a continuous function.

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