Question
For the following function, find \( f(2.1) \) and \( f(4) \).
\( f(x)=\left\{\begin{array}{ll}2 x-3, & 0
Ask by Vega Carlson. in the United States
Jan 02,2025
Ask by Vega Carlson. in the United States
Jan 02,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(2.1) = 2.205 \) and \( f(4) = 2 \).
Solution
To determine \( f(2.1) \) and \( f(4) \) for the given piecewise function:
\[
f(x)=
\begin{cases}
2x - 3 & \text{if } 0 < x \leq 2 \\
\frac{1}{2}x^2 & \text{if } 2 < x < 4 \\
\log_2 x & \text{if } 4 \leq x < 8
\end{cases}
\]
1. **For \( f(2.1) \):**
- \( 2.1 \) falls in the interval \( 2 < x < 4 \).
- \( f(2.1) = \frac{1}{2} \times (2.1)^2 = \frac{1}{2} \times 4.41 = 2.205 \).
2. **For \( f(4) \):**
- \( 4 \) falls in the interval \( 4 \leq x < 8 \).
- \( f(4) = \log_2(4) = 2 \).
**Answer:**
\( f(2.1)=2.205 \) and \( f(4)=2 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find \( f(2.1) \) and \( f(4) \), we need to look at the piecewise function given. For \( x = 2.1 \): Since \( 2 < x < 4 \), we use the second piece of the function: \( f(x) = \frac{1}{2}x^2 \). Calculating \( f(2.1) \): \[ f(2.1) = \frac{1}{2}(2.1)^2 = \frac{1}{2}(4.41) = 2.205 \] For \( x = 4 \): Since \( 4 \leq x < 8 \), we use the third piece of the function: \( f(x) = \log_2 x \). Calculating \( f(4) \): \[ f(4) = \log_2(4) = 2 \] So, \( f(2.1) = 2.205 \) and \( f(4) = 2 \). The correct answer is: \( f(2.1) = 2.205 \) and \( f(4) = 2 \).
