Math Problem Statement
Find f(0) for the piece-wise function: f(x) = {x + 2 if x ≤ -1, 2x + 4 if x > -1}
Solution
Let's solve the given piece-wise function for .
The function is defined as:
\begin{cases} x + 2 & \text{if } x \leq -1 \\ 2x + 4 & \text{if } x > -1 \end{cases}$$ We are asked to find $$f(0)$$. Since $$0 > -1$$, we will use the second part of the piece-wise function: $$f(x) = 2x + 4 \quad \text{for} \quad x > -1.$$ Substitute $$x = 0$$: $$f(0) = 2(0) + 4 = 0 + 4 = 4.$$ So, $$f(0) = 4$$. Would you like more details on this solution, or do you have any other questions? --- Here are 5 related questions to expand your understanding: 1. How would you evaluate $$f(-2)$$ using the same piece-wise function? 2. What happens to the function $$f(x)$$ as $$x$$ approaches -1 from the left and right? 3. How can you graph this piece-wise function? 4. What would the value of $$f(1)$$ be? 5. How would you rewrite this piece-wise function for all real numbers? **Tip:** When dealing with piece-wise functions, always check which condition your input falls under before substituting into the equation.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Substitution
Formulas
f(x) = {x + 2 if x ≤ -1, 2x + 4 if x > -1}
Theorems
Piecewise Function Substitution
Suitable Grade Level
Grades 9-12