Respuesta :
Using the definition of the absolute value function, the piece-wise function is:
[tex]f(x) = 2x + 3, x \geq -\frac{3}{2}[/tex]
[tex]f(x) = -2x - 3, x < -\frac{3}{2}[/tex]
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The definition of the absolute value function is given by:
[tex]|g(x)| = g(x), g(x) \geq 0[/tex]
[tex]|g(x)| = -g(x), g(x) < 0[/tex]
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In this question, we have:
[tex]g(x) = 2x + 3[/tex]
Finding where it is positive/negative:
[tex]g(x) \geq 0[/tex]
[tex]2x + 3 \geq 0[/tex]
[tex]2x \geq -3[/tex]
[tex]x \geq -\frac{3}{2}[/tex]
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[tex]g(x) = 2x + 3, -g(x) = -(2x + 3) = -2x - 3[/tex]
Thus, the piece-wise function is:
[tex]f(x) = 2x + 3, x \geq -\frac{3}{2}[/tex]
[tex]f(x) = -2x - 3, x < -\frac{3}{2}[/tex]
A similar problem is given at https://brainly.com/question/24514895
