Let (A) Find an Expression for G (X) Similar to the l

question 4

Essay

Let $$f ( x ) = \left\{ \begin{array} { l l l } 0 & \text { if } & x < 0 \\2 x & \text { if } & 0 \leq x \leq 1 \text { and } g ( x ) = \int _ { 0 } ^ { x } f ( t ) d t . \\2 & \text { if } & 1 < x\end{array} \right.$$ (a) Find an expression for g (x) similar to the one for f (x).(b) Where is f differentiable? Where is g differentiable?

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Definitions:

Labor Force Participation Rate

The percentage of the population ages 16 and over that is working or actively seeking work.

Adult Population

A demographic group consisting of individuals who have reached the age where they are legally recognized as adults, important for analyses related to labor, voting, and consumption.

Labor Force Participation Rate

The percentage of the working-age population that is working or actively looking for work, indicating the level of active engagement in the labor market.

Cyclical Unemployment

Cyclical unemployment refers to the fluctuation in unemployment that occurs due to the ups and downs of the economy over time.