Math Problem Statement
Diketahui f(x) = (1/x jika x > 3, 2x jika x ≤ 3). Tentukan nilai dari: a. f(-4), b. f(0), c. f(t^2 + 5)
Solution
We are given a piecewise function :
\begin{cases} \frac{1}{x}, & \text{jika } x > 3 \\ 2x, & \text{jika } x \leq 3 \end{cases}$$ We are asked to determine the values of: 1. $$f(-4)$$ 2. $$f(0)$$ 3. $$f(t^2 + 5)$$ ### a. $$f(-4)$$ Since $$-4 \leq 3$$, we use the second part of the function, $$f(x) = 2x$$. Thus: $$f(-4) = 2(-4) = -8$$ ### b. $$f(0)$$ Since $$0 \leq 3$$, we again use $$f(x) = 2x$$. Thus: $$f(0) = 2(0) = 0$$ ### c. $$f(t^2 + 5)$$ We need to determine which part of the function applies to $$f(t^2 + 5)$$. Since $$t^2 + 5 > 3$$ for any real number $$t$$, we use the first part of the function, $$f(x) = \frac{1}{x}$$. Thus: $$f(t^2 + 5) = \frac{1}{t^2 + 5}$$ ### Final Answers: a. $$f(-4) = -8$$ b. $$f(0) = 0$$ c. $$f(t^2 + 5) = \frac{1}{t^2 + 5}$$ Would you like further details or have any questions? Here are five related questions for deeper understanding: 1. What happens if $$t = -2$$ in part c? 2. How does the behavior of the piecewise function change around $$x = 3$$? 3. What is $$f(5)$$ based on the given function? 4. How would you express $$f(x)$$ if $$x = 3$$? 5. Can you find the derivative of $$f(x)$$ for $$x > 3$$? **Tip:** Always check the conditions in a piecewise function carefully before selecting the right expression for a given input.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Function
Function Evaluation
Formulas
f(x) = 1/x jika x > 3
f(x) = 2x jika x ≤ 3
Theorems
Definition of Piecewise Functions
Suitable Grade Level
Grades 10-12