Math Problem Statement
Given f(x) =
{9-x2, x<2
{ √x +7, 2≤x<10
{[x-4] ,x ≥ 10
(a) f(2)
Solution
To find , we need to determine which part of the piecewise function applies when .
The function is defined as:
\begin{cases} 9 - x^2, & \text{if } x < 2 \\ \sqrt{x} + 7, & \text{if } 2 \leq x < 10 \\ |x - 4|, & \text{if } x \geq 10 \end{cases}$$ Since $$x = 2$$ falls in the interval $$2 \leq x < 10$$, we use the second piece of the function: $$f(x) = \sqrt{x} + 7$$ Now, plug in $$x = 2$$: $$f(2) = \sqrt{2} + 7$$ $$f(2) = \sqrt{2} + 7 \approx 1.414 + 7 = 8.414$$ Therefore, $$f(2) = \sqrt{2} + 7$$. Would you like more details or have any questions? Here are 5 related questions to expand on this topic: 1. What is $$f(10)$$ for the given function? 2. How do you find $$f(x)$$ for values less than 2? 3. What is the domain of the function $$f(x)$$? 4. How would you graph this piecewise function? 5. What are the intervals where $$f(x)$$ is continuous? **Tip:** When working with piecewise functions, always pay attention to the conditions for each piece to determine which part of the function to use for specific values of $$x$$.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Square Root Function
Absolute Value Function
Formulas
-
Theorems
-
Suitable Grade Level
Grades 10-12