Question
find the invers function in slope intercept form mx+b
f(x)=-x-2
f^-1 (x)=
solve for a cookie
f(x)=-x-2
f^-1 (x)=
solve for a cookie
Answers
GPT-4o mini
To find the inverse function \( f^{-1}(x) \) of \( f(x) = -x - 2 \), we can follow these steps:
1. **Replace \( f(x) \) with \( y \)**:
\[
y = -x - 2
\]
2. **Swap \( x \) and \( y \)**:
\[
x = -y - 2
\]
3. **Solve for \( y \)**:
\[
x + 2 = -y
\]
\[
-y = x + 2
\]
\[
y = -x - 2
\]
So the inverse function is:
\[
f^{-1}(x) = -x - 2
\]
The result for the inverse function \( f^{-1}(x) \) is:
\[
f^{-1}(x) = -x - 2
\]
### Writing in Slope-Intercept Form:
The form \( mx + b \) is already obtained since the function is linear with a slope \( m = -1 \) and a y-intercept \( b = -2 \).
### "Solve for a cookie":
If by "solve for a cookie" you meant just to express the answer lightly or humorously, you might simply consider that once you take the inverse \( f^{-1}(x) \), you might reward yourself with a cookie! If you meant something specific by that phrase, please provide more context!
1. **Replace \( f(x) \) with \( y \)**:
\[
y = -x - 2
\]
2. **Swap \( x \) and \( y \)**:
\[
x = -y - 2
\]
3. **Solve for \( y \)**:
\[
x + 2 = -y
\]
\[
-y = x + 2
\]
\[
y = -x - 2
\]
So the inverse function is:
\[
f^{-1}(x) = -x - 2
\]
The result for the inverse function \( f^{-1}(x) \) is:
\[
f^{-1}(x) = -x - 2
\]
### Writing in Slope-Intercept Form:
The form \( mx + b \) is already obtained since the function is linear with a slope \( m = -1 \) and a y-intercept \( b = -2 \).
### "Solve for a cookie":
If by "solve for a cookie" you meant just to express the answer lightly or humorously, you might simply consider that once you take the inverse \( f^{-1}(x) \), you might reward yourself with a cookie! If you meant something specific by that phrase, please provide more context!