Math Problem Statement
f(x)={ x 2 +1 1
for x<1 1 1
for x≥4 1 1
Find , f, of, 5 Find f(5)
Solution
The function is defined as a piecewise function with two parts:
\begin{cases} x^2 + 1 & \text{for } x < 1 \\ 1 & \text{for } x \geq 4 \end{cases}$$ To find $$f(5)$$, we need to check which condition applies for $$x = 5$$. Since $$5 \geq 4$$, we use the second part of the function, which is $$f(x) = 1$$ for $$x \geq 4$$. Thus, $$f(5) = 1$$. ### Would you like a more detailed explanation or have further questions? Here are 5 related questions you can explore: 1. What would $$f(0)$$ be? 2. How do you handle piecewise functions with more than two parts? 3. What is the general process to evaluate a piecewise function at a specific point? 4. How would you find the limit of a piecewise function at a boundary point like $$x = 1$$? 5. Can piecewise functions be continuous across all intervals? **Tip:** Always carefully check the condition of the piecewise function that corresponds to your input value to ensure you're using the correct formula.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
f(x) = { x^2 + 1 for x < 1; 1 for x ≥ 4
Theorems
Piecewise Function Definition
Suitable Grade Level
Grades 8-10