Question
Jane completed 8 homework problems in class.
The function p(m) relates the time (in minutes)
Jane spent on her homework at home to the total number of problems she completed. The input is the number of minutes worked. The output is the number of problems completed.
P(m) = 품 +8
Which equation represents the inverse function m(p), which uses problems completed as the input and gives minutes worked as the output?
0 m(p) = 5p + 40
O m(p) =40p 5
0 m(p) = 5p - 40
Om(p) =40p+5
The function p(m) relates the time (in minutes)
Jane spent on her homework at home to the total number of problems she completed. The input is the number of minutes worked. The output is the number of problems completed.
P(m) = 품 +8
Which equation represents the inverse function m(p), which uses problems completed as the input and gives minutes worked as the output?
0 m(p) = 5p + 40
O m(p) =40p 5
0 m(p) = 5p - 40
Om(p) =40p+5
Answers
Answered by
GPT-4o mini
To find the inverse function \( m(p) \) from the function \( p(m) = 5m + 8 \), we need to solve for \( m \) in terms of \( p \).
1. Start with the original function:
\[
p(m) = 5m + 8
\]
2. Set \( p \) equal to \( p(m) \):
\[
p = 5m + 8
\]
3. Isolate \( m \):
\[
p - 8 = 5m
\]
4. Divide both sides by 5:
\[
m = \frac{p - 8}{5}
\]
Now we have the inverse function:
\[
m(p) = \frac{p - 8}{5}
\]
To express this in a form that resembles the options given, you can rewrite it:
\[
m(p) = \frac{1}{5}p - \frac{8}{5}
\]
None of the original options directly match this result, but let's analyze the options you provided to see if there is a mistake in our functions or response formatting.
The function options you gave were:
1. \( m(p) = 5p + 40 \)
2. \( m(p) = 40p - 5 \)
3. \( m(p) = 5p - 40 \)
4. \( m(p) = 40p + 5 \)
None of these match \( m(p) = \frac{p - 8}{5} \).
Let's check if I made an error in understanding or if any adaptations of \( m(p) \) could lead to one of the given options, but directly, the result \( m(p) = \frac{p - 8}{5} \) appears to stand correct.
If there has been a transposing error in how options were presented or issues with factor relating, it might be worth revisiting the primary function or ensuring the right equations were selected as options. If you recheck your source, I can further analyze possibilities based on that context.
1. Start with the original function:
\[
p(m) = 5m + 8
\]
2. Set \( p \) equal to \( p(m) \):
\[
p = 5m + 8
\]
3. Isolate \( m \):
\[
p - 8 = 5m
\]
4. Divide both sides by 5:
\[
m = \frac{p - 8}{5}
\]
Now we have the inverse function:
\[
m(p) = \frac{p - 8}{5}
\]
To express this in a form that resembles the options given, you can rewrite it:
\[
m(p) = \frac{1}{5}p - \frac{8}{5}
\]
None of the original options directly match this result, but let's analyze the options you provided to see if there is a mistake in our functions or response formatting.
The function options you gave were:
1. \( m(p) = 5p + 40 \)
2. \( m(p) = 40p - 5 \)
3. \( m(p) = 5p - 40 \)
4. \( m(p) = 40p + 5 \)
None of these match \( m(p) = \frac{p - 8}{5} \).
Let's check if I made an error in understanding or if any adaptations of \( m(p) \) could lead to one of the given options, but directly, the result \( m(p) = \frac{p - 8}{5} \) appears to stand correct.
If there has been a transposing error in how options were presented or issues with factor relating, it might be worth revisiting the primary function or ensuring the right equations were selected as options. If you recheck your source, I can further analyze possibilities based on that context.