Questions: Suppose that the function (g) is defined, for all real numbers, as follows. [g(x)=leftbeginarrayll frac12 x-1 text if x neq-2 1 text if x=-2 endarrayright.] Find (g(-5), g(-2)), and (g(5)). [ beginarrayc g(-5)=square g(-2)=square g(5)=square endarray ]

$Suppose that the function (g) is defined, for all real numbers, as follows. [g(x)=leftbeginarrayll frac12 x-1 text if x neq-2 1 text if x=-2 endarrayright.] Find (g(-5), g(-2)), and (g(5)). [ beginarrayc g(-5)=square g(-2)=square g(5)=square endarray ]$

Transcript text: Suppose that the function $g$ is defined, for all real numbers, as follows. \[ g(x)=\left\{\begin{array}{ll} \frac{1}{2} x-1 & \text { if } x \neq-2 \\ 1 & \text { if } x=-2 \end{array}\right. \] Find $g(-5), g(-2)$, and $g(5)$. \[ \begin{array}{c} g(-5)=\square \\ g(-2)=\square \\ g(5)=\square \end{array} \]

Solution

Solution Steps

To find the values of the function $ g $ at specific points, we need to evaluate the piecewise function for each given input. For $ g(-5) $ and $ g(5) $, we use the expression $\frac{1}{2}x - 1$ since these values are not equal to $-2$. For $ g(-2) $, we use the value $1$ as specified by the function definition for $ x = -2 $.

Step 1: Evaluate $ g(-5) $

To find $ g(-5) $, we use the piecewise definition of the function: \[ g(-5) = \frac{1}{2}(-5) - 1 = -\frac{5}{2} - 1 = -\frac{5}{2} - \frac{2}{2} = -\frac{7}{2} = -3.5 \]

Step 2: Evaluate $ g(-2) $

For $ g(-2) $, we directly use the value defined in the piecewise function: \[ g(-2) = 1 \]

Step 3: Evaluate $ g(5) $

To find $ g(5) $, we again use the piecewise definition: \[ g(5) = \frac{1}{2}(5) - 1 = \frac{5}{2} - 1 = \frac{5}{2} - \frac{2}{2} = \frac{3}{2} = 1.5 \]

Final Answer

The values are: \[ g(-5) = -3.5, \quad g(-2) = 1, \quad g(5) = 1.5 \] Thus, the final boxed answers are: \[ \boxed{g(-5) = -3.5}, \quad \boxed{g(-2) = 1}, \quad \boxed{g(5) = 1.5} \]

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