Math Problem Statement
If f(x)={−2x−3x2−2xififx<3x≥3 , what is f(t+2) when t=2 ?
A. 8 B. 0 C. -5 D. -1
Solution
The function is defined in a piecewise manner as:
\begin{cases} -2x - 3x^2 - 2x & \text{if } x < 3 \\ x & \text{if } x \geq 3 \end{cases}$$ We need to find $$f(t+2)$$ when $$t = 2$$. ### Step 1: Substitute $$t = 2$$ into $$f(t+2)$$ This gives us $$f(2+2) = f(4)$$. ### Step 2: Determine which part of the piecewise function to use for $$x = 4$$ Since $$4 \geq 3$$, we use the second part of the piecewise function: $$f(x) = x \quad \text{for} \quad x \geq 3$$ Thus, $$f(4) = 4$$. ### Step 3: Conclusion The value of $$f(t+2)$$ when $$t = 2$$ is $$4$$. However, none of the provided options (A. 8, B. 0, C. -5, D. -1) is correct. Based on the calculations, it seems that the answer should be **4**, but this was not listed as an option. If there's any error or confusion about the function definition or options, feel free to clarify. Would you like further explanation on this problem? Or any other questions? Here are some related questions for you to explore: 1. How do you handle piecewise functions in general? 2. How do you graph piecewise functions? 3. What happens if you switch the inequalities in piecewise functions? 4. How do you evaluate limits of piecewise functions? 5. How would the answer change if the condition for the second piece of the function was $$x \leq 3$$? **Tip**: Always check whether the boundary condition (like $$x = 3$$) falls under the inequality before deciding which part of the function to apply.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Inequalities
Formulas
f(x) = -2x - 3x^2 - 2x (if x < 3)
f(x) = x (if x >= 3)
Theorems
Piecewise function evaluation
Suitable Grade Level
Grades 9-11