Question
The graphs of two linear functions f and g are shown in the following figure. (Domains are all real numbers.)
(a) Solve the equation f(x)equalsg(x).
(b) Solve the inequality f(x)less than or equalsg(x).
Question content area bottom left
Part 1
(a) The solution for f(x)equalsg(x) is
enter your response here.
(Simplify your answer.)
Part 2
(b) The solution for f(x)less than or equalsg(x) is
enter your response here.
share point 1,1
(a) Solve the equation f(x)equalsg(x).
(b) Solve the inequality f(x)less than or equalsg(x).
Question content area bottom left
Part 1
(a) The solution for f(x)equalsg(x) is
enter your response here.
(Simplify your answer.)
Part 2
(b) The solution for f(x)less than or equalsg(x) is
enter your response here.
share point 1,1
Answers
GPT-4o mini
To solve the given problems, we need to determine the functions \( f(x) \) and \( g(x) \) based on their graphs. Since you mentioned the point (1,1) and the equations are linear functions, let's assume the functions can be represented in slope-intercept form:
1. **Determine the equations:**
- Let's assume the equations of these functions based on the typical graph shapes. Without a visual, I will demonstrate how to proceed with common scenarios.
- Suppose:
\[
f(x) = mx + b_1 \quad \text{(for function \( f \))}
\]
\[
g(x) = nx + b_2 \quad \text{(for function \( g \))}
\]
2. **Solve \( f(x) = g(x) \) (Part 1):**
- Set the two equations equal to each other:
\[
mx + b_1 = nx + b_2
\]
- Rearranging gives:
\[
(m - n)x = b_2 - b_1
\]
- Therefore,
\[
x = \frac{b_2 - b_1}{m - n} \quad \text{(if \( m \neq n \))}
\]
3. **Solve \( f(x) \leq g(x) \) (Part 2):**
- For the inequality:
\[
mx + b_1 \leq nx + b_2
\]
- Rearranging gives:
\[
(m - n)x \leq b_2 - b_1
\]
- If \( m - n > 0 \):
\[
x \leq \frac{b_2 - b_1}{m - n}
\]
- If \( m - n < 0 \):
\[
x \geq \frac{b_2 - b_1}{m - n}
\]
4. **Conclusion:**
- The solutions will depend on the specific coefficients and points on the graph provided in your figure.
- To finalize, you can insert the actual values of \( m, n, b_1, \) and \( b_2 \) from your graph to compute those exact solutions.
If you can provide more details about the functions or more points on the graph, I'll be able to give you the specific numerical answers.
1. **Determine the equations:**
- Let's assume the equations of these functions based on the typical graph shapes. Without a visual, I will demonstrate how to proceed with common scenarios.
- Suppose:
\[
f(x) = mx + b_1 \quad \text{(for function \( f \))}
\]
\[
g(x) = nx + b_2 \quad \text{(for function \( g \))}
\]
2. **Solve \( f(x) = g(x) \) (Part 1):**
- Set the two equations equal to each other:
\[
mx + b_1 = nx + b_2
\]
- Rearranging gives:
\[
(m - n)x = b_2 - b_1
\]
- Therefore,
\[
x = \frac{b_2 - b_1}{m - n} \quad \text{(if \( m \neq n \))}
\]
3. **Solve \( f(x) \leq g(x) \) (Part 2):**
- For the inequality:
\[
mx + b_1 \leq nx + b_2
\]
- Rearranging gives:
\[
(m - n)x \leq b_2 - b_1
\]
- If \( m - n > 0 \):
\[
x \leq \frac{b_2 - b_1}{m - n}
\]
- If \( m - n < 0 \):
\[
x \geq \frac{b_2 - b_1}{m - n}
\]
4. **Conclusion:**
- The solutions will depend on the specific coefficients and points on the graph provided in your figure.
- To finalize, you can insert the actual values of \( m, n, b_1, \) and \( b_2 \) from your graph to compute those exact solutions.
If you can provide more details about the functions or more points on the graph, I'll be able to give you the specific numerical answers.