Math Problem Statement
solve this
Calculate the following values using the given piecewise function: g(x) = { 10x + 5 if x < 0 ; -3x + 8 if 0 ≤ x < 10 }
Solution
Let's solve the given problems step by step based on the piecewise function :
\begin{cases} 10x + 5 & \text{if } x < 0 \\ -3x + 8 & \text{if } 0 \leq x < 10 \end{cases}$$ ### A) The value of $$g(-10)$$: - Since $$-10 < 0$$, we use the first part of the function: $$g(x) = 10x + 5$$. $$g(-10) = 10(-10) + 5 = -100 + 5 = -95$$ So, the correct option is not available. But based on the function definition, $$g(-10) = -95$$. ### B) $$g(0)$$: - Since $$0 \leq 0 < 10$$, we use the second part of the function: $$g(x) = -3x + 8$$. $$g(0) = -3(0) + 8 = 0 + 8 = 8$$ So, $$g(0) = 8$$. ### C) $$g(7)$$: - Since $$0 \leq 7 < 10$$, we use the second part of the function: $$g(x) = -3x + 8$$. $$g(7) = -3(7) + 8 = -21 + 8 = -13$$ So, $$g(7) = -13$$. ### D) The value of $$g(17)$$: - Since $$17 \geq 10$$, 17 is not in the domain of the function. The domain of the function is $$(-\infty, 10)$$, meaning the function does not have any value for $$g(17)$$. Thus, the correct option is: "It is not defined, because 17 is not in the domain of $$g$$." --- Let me know if you'd like further clarification or have any more questions. Here are some related questions: 1. How do you find the domain of a piecewise function? 2. What are the key steps to solving piecewise functions? 3. Can you describe how to graph the piecewise function given here? 4. How would the function change if the domain included $$x \geq 10$$? 5. Can you solve for $$g(x)$$ when $$x = -5$$? **Tip**: Always carefully analyze the conditions of piecewise functions to ensure you are applying the correct formula for each interval.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
g(x) = 10x + 5 when x < 0
g(x) = -3x + 8 when 0 ≤ x < 10
Theorems
-
Suitable Grade Level
Grades 9-12
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