$\text { Find all values of } c \text { such that } f \text { is continuous on } ( - \infty , \infty ) \text {. }$

question 49

Multiple Choice

$\text { Find all values of } c \text { such that } f \text { is continuous on } ( - \infty , \infty ) \text {. }$ $$f ( x ) = \left\{ \begin{array} { l l } 4 - x ^ { 2 } , & x \leq c \\x , & x > c\end{array} \right.$$

• A) \(c = 3\)
• B) \(c = 0\)
• C) \(\frac { - 1 + \sqrt { 17 } } { 2 }\)
• D) \(\frac { 1 + \sqrt { 17 } } { 2 } , \frac { 1 - \sqrt { 17 } } { 2 }\)
• E) \(\frac { - 1 + \sqrt { 17 } } { 2 } , \frac { - 1 - \sqrt { 17 } } { 2 }\)

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Definitions:

Military Strength

The total capacity and capability of a nation's armed forces, including personnel, weaponry, equipment, and strategic proficiency, to defend itself or engage in warfare.

Moral Imperialism

The imposition of a nation's perceived moral standards and values upon another country or people, often used to justify imperialism and colonization.

Military Interventions

Military interventions are actions undertaken by a nation's military forces to intervene in the affairs of another country, often to enforce international mandates, protect interests, or support allies.

Stability

The state of being steady and unchanging, often used to describe economic, political, or social conditions that are consistently reliable and free from upheaval or disorder.