Question
Check the points where the constant function f(x) = k is continuous.
✓
Answer
The function is defined at all real numbers and by definition, its value at any real number equals k.
Let c be any real number. Then
$\mathop {\lim }\limits_{x \to c} f(x) = \mathop {\lim }\limits_{x \to c} $ k = k
Since f(c) = k = $\mathop {\lim }\limits_{x \to c} f(x)$ for any real number c, the function f is continuous at every real number.
Let c be any real number. Then
$\mathop {\lim }\limits_{x \to c} f(x) = \mathop {\lim }\limits_{x \to c} $ k = k
Since f(c) = k = $\mathop {\lim }\limits_{x \to c} f(x)$ for any real number c, the function f is continuous at every real number.
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