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Review the graph of the function f(x). Which statement describes the continuity of the function at x = 1?

The function is only left-continuous at x = 1.
The function is only right-continuous at x = 1.
The function is both left-continuous and right-continuous at x = 1.
The function is neither left-continuous nor right-continuous at x = 1.

Review the graph of the function fx Which statement describes the continuity of the function at x 1 The function is only leftcontinuous at x 1 The function is o class=

Respuesta :

Using continuity concepts, it is found that:

The function is only left-continuous at x = 1.

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A function f(x) is said to be continuous at x = a if:

[tex]\lim_{x \rightarrow a^{-}} f(x) = \lim_{x \rightarrow a^{+}} f(x) = f(a)[/tex]

  • If only [tex]\lim_{x \rightarrow a^{-}} f(x) = f(a)[/tex], the function is left-continuous.
  • If only [tex]\lim_{x \rightarrow a^{+}} f(x) = f(a)[/tex], the function is right-continuous.

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In this question, the function is defined only to the left of [tex]x = 1[/tex]. Since [tex]\lim_{x \rightarrow 1^{-}} f(x) = f(1)[/tex], the function is only left-continuous, and the correct option is:

The function is only left-continuous at x = 1.

A similar problem is given at https://brainly.com/question/17007671

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