https://file.aiquickdraw.com/mathbot/file/1725466567900wd9pvorf.jpg

The given problem asks to evaluate \( g(x) = \frac{x-7}{x+2} \) at several values of \( x \). Let's break down the steps and solve each:

The function is:
\[
g(x) = \frac{x - 7}{x + 2}
\]

### a) \( g(0) \)
Substitute \( x = 0 \) into the function:
\[
g(0) = \frac{0 - 7}{0 + 2} = \frac{-7}{2} = -\frac{7}{2}
\]

### b) \( g(-2) \)
Substitute \( x = -2 \) into the function:
\[
g(-2) = \frac{-2 - 7}{-2 + 2} = \frac{-9}{0}
\]
Since division by zero is undefined, \( g(-2) \) does not exist.

### c) \( g(-17.75) \)
Substitute \( x = -17.75 \) into the function:
\[
g(-17.75) = \frac{-17.75 - 7}{-17.75 + 2} = \frac{-24.75}{-15.75} = \frac{24.75}{15.75} \approx 1.5714
\]

### d) \( g(a + 1) \)
Substitute \( x = a + 1 \) into the function:
\[
g(a + 1) = \frac{a + 1 - 7}{a + 1 + 2} = \frac{a - 6}{a + 3}
\]

---

Let's review the options for each part:

For part **(b)**, where \( g(-2) \), the correct choice is:
- \( g(-2) \) does not exist because division by zero is undefined.

Would you like further clarification on any part or detailed steps? Also, here are some related questions to deepen your understanding:

1. How can we identify when a function is undefined?
2. What happens to a rational function when the denominator is zero?
3. How do you evaluate a function at any real number or variable?
4. What does it mean for a function to be continuous at a point?
5. Can you find where \( g(x) \) is equal to 1?

**Tip**: Always check the denominator in a rational function before substituting values to avoid division by zero.

Given the function g(x) = (x - 7) / (x + 2), find each of the following: g(0), g(-2), g(-17.75), g(a + 1).

Learn how to evaluate the rational function g(x) = (x - 7) / (x + 2) at different values, including when the function becomes undefined. This solution covers key algebraic concepts related to function evaluation and undefined expressions, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation