Tran Maxwell
03/07/2024 · Junior High School
Evaluate the piecewise function *
1) \( f(x)=\left\{\begin{array}{ll}-x-4 & , x \leq 5 \\ 2 x^{2}-7 & , 5
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To evaluate the piecewise function \( f(x) \), we need to determine which piece of the function to use based on the value of \( x \).
1) The function is defined as:
\[
f(x) =
\begin{cases}
-x - 4 & \text{if } x \leq 5 \\
2x^2 - 7 & \text{if } 5 < x \leq 10
\end{cases}
\]
Now, let's evaluate the function for the given values:
i) For \( f(-2) \):
- Since \(-2 \leq 5\), we use the first piece of the function:
\[
f(-2) = -(-2) - 4 = 2 - 4 = -2
\]
ii) For \( f(7) \):
- Since \(7 > 5\) and \(7 \leq 10\), we use the second piece of the function:
\[
f(7) = 2(7^2) - 7 = 2(49) - 7 = 98 - 7 = 91
\]
Thus, the evaluations are:
i) \( f(-2) = -2 \)
ii) \( f(7) = 91 \)
Quick Answer
i) \( f(-2) = -2 \)
ii) \( f(7) = 91 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit