Suppose that the function g is defined, for all real numbers, as follows. 1 -x+2 if x #1 g(x): -3 Find g (-1), g(1), and g (3). 8 (-1) = [] g g(1) = g (3) = if x = 1 X Ś
Suppose that the function g is defined, for all real numbers, as follows. 1 -x+2 if x #1 g(x): -3 Find g (-1), g(1), and g (3). 8 (-1) = [] g g(1) = g (3) = if x = 1 X Ś
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![### Understanding Piecewise Functions
Suppose that the function \( g \) is defined, for all real numbers, as follows:
\[
g(x) = \begin{cases}
\frac{1}{4} x + 2 & \text{if } x \neq 1 \\
-3 & \text{if } x = 1
\end{cases}
\]
### Problem Statement
**Find \( g(-1) \), \( g(1) \), and \( g(3) \).**
The values you need to compute are shown as follows:
1. \( g(-1) = \)
2. \( g(1) = \)
3. \( g(3) = \)
### Explanation
To find these values, follow these steps:
1. **Evaluate \( g(-1) \):**
- Since \(-1 \neq 1\), we use \( g(x) = \frac{1}{4} x + 2 \).
- Substitute \( x = -1 \):
\[
g(-1) = \frac{1}{4} (-1) + 2 = -\frac{1}{4} + 2 = \frac{7}{4}
\]
2. **Evaluate \( g(1) \):**
- For \( x = 1 \), the function is defined as:
\[
g(1) = -3
\]
3. **Evaluate \( g(3) \):**
- Since \( 3 \neq 1\), we use \( g(x) = \frac{1}{4} x + 2 \).
- Substitute \( x = 3 \):
\[
g(3) = \frac{1}{4} (3) + 2 = \frac{3}{4} + 2 = \frac{11}{4}
\]
### Conclusion
The results are:
\[
\begin{align*}
g(-1) &= \frac{7}{4} \\
g(1) &= -3 \\
g(3) &= \frac{11}{4}
\end{align*}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a663202-2562-419a-bf45-34f83e9296f9%2F7c9fff34-728e-4963-857d-facdae349437%2Foof4s1q_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Piecewise Functions
Suppose that the function \( g \) is defined, for all real numbers, as follows:
\[
g(x) = \begin{cases}
\frac{1}{4} x + 2 & \text{if } x \neq 1 \\
-3 & \text{if } x = 1
\end{cases}
\]
### Problem Statement
**Find \( g(-1) \), \( g(1) \), and \( g(3) \).**
The values you need to compute are shown as follows:
1. \( g(-1) = \)
2. \( g(1) = \)
3. \( g(3) = \)
### Explanation
To find these values, follow these steps:
1. **Evaluate \( g(-1) \):**
- Since \(-1 \neq 1\), we use \( g(x) = \frac{1}{4} x + 2 \).
- Substitute \( x = -1 \):
\[
g(-1) = \frac{1}{4} (-1) + 2 = -\frac{1}{4} + 2 = \frac{7}{4}
\]
2. **Evaluate \( g(1) \):**
- For \( x = 1 \), the function is defined as:
\[
g(1) = -3
\]
3. **Evaluate \( g(3) \):**
- Since \( 3 \neq 1\), we use \( g(x) = \frac{1}{4} x + 2 \).
- Substitute \( x = 3 \):
\[
g(3) = \frac{1}{4} (3) + 2 = \frac{3}{4} + 2 = \frac{11}{4}
\]
### Conclusion
The results are:
\[
\begin{align*}
g(-1) &= \frac{7}{4} \\
g(1) &= -3 \\
g(3) &= \frac{11}{4}
\end{align*}
\]
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