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Consider the piecewise function:

$$f(x) = \left\{ {\begin{array}{*{20}{c}} {5{x^2} - 2}&{x > 1}\\\ {{x^2} + 2}&{x < 1} \end{array}} \right.$$

For what value, if any, is $f(x)$ discontinuous?

Describe the type of discontinuity if one exists.

A

Discontinuous at $x=1$; removable point discontinuity.

B

Discontinuous at $x=1$; non-removable point discontinuity.

C

Discontinuous at $x=1$; non-removable jump discontinuity.

D

The function $f(x)$ is continuous everywhere.

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