Math Problem Statement
Use the given function:f(x) = {x+3,−x3,if 0≤x<2if 2≤x≤5Find the value of f(3)
Solution
The given function is defined piecewise as follows:
\begin{cases} x + 3 & \text{if } 0 \leq x < 2 \\ -x^3 & \text{if } 2 \leq x \leq 5 \end{cases}$$ We are asked to find $$f(3)$$. 1. Since $$3$$ is within the interval $$2 \leq x \leq 5$$, we use the second part of the piecewise function: $$f(x) = -x^3$$ 2. Substituting $$x = 3$$ into this expression: $$f(3) = -(3)^3 = -27$$ Thus, $$f(3) = -27$$. Would you like further details or have any questions? Here are some related questions for further practice: 1. What is the value of $$f(1)$$? 2. What is the value of $$f(2)$$? 3. What is the domain of the function $$f(x)$$? 4. Is $$f(x)$$ continuous at $$x = 2$$? 5. Can you graph the function $$f(x)$$? **Tip:** When dealing with piecewise functions, always check which part of the function applies to the given input based on its domain.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Polynomial Functions
Evaluation of Functions
Formulas
f(x) = x + 3, if 0 ≤ x < 2
f(x) = -x^3, if 2 ≤ x ≤ 5
Theorems
Definition of Piecewise Functions
Basic Polynomial Evaluation
Suitable Grade Level
Grades 9-11