Math Problem Statement
Дано функцію g(x) = { x^2, якщо x ≤ -1; x + 5, якщо x > -1 }. Знайдіть g(-3); g(-1); g(0); g(2).
Solution
The function given in the image is a piecewise function:
\begin{cases} x^2, & \text{if } x \leq -1 \\ x + 5, & \text{if } x > -1 \end{cases}$$ We are asked to find the values of $$g(-3)$$, $$g(-1)$$, $$g(0)$$, and $$g(2)$$. ### Solution: 1. **$$g(-3)$$**: Since $$-3 \leq -1$$, we use the first part of the piecewise function: $$g(-3) = (-3)^2 = 9$$ 2. **$$g(-1)$$**: Since $$-1 \leq -1$$, we again use the first part of the piecewise function: $$g(-1) = (-1)^2 = 1$$ 3. **$$g(0)$$**: Since $$0 > -1$$, we use the second part of the piecewise function: $$g(0) = 0 + 5 = 5$$ 4. **$$g(2)$$**: Since $$2 > -1$$, we use the second part of the piecewise function: $$g(2) = 2 + 5 = 7$$ ### Final Answers: - $$g(-3) = 9$$ - $$g(-1) = 1$$ - $$g(0) = 5$$ - $$g(2) = 7$$ Do you want further details on how piecewise functions work? Here are some related questions to explore: 1. What are the general properties of piecewise functions? 2. How do you graph a piecewise function? 3. Can a piecewise function have more than two conditions? 4. How do you find the domain and range of a piecewise function? 5. What is the significance of continuity in piecewise functions? **Tip:** When evaluating piecewise functions, always pay close attention to the conditions that specify the intervals for different expressions.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Quadratic Functions
Linear Functions
Formulas
g(x) = x^2 for x ≤ -1
g(x) = x + 5 for x > -1
Theorems
Basic properties of piecewise functions
Suitable Grade Level
Grades 9-11