Question

find the invers function in slope intercept form mx+b
f(x)=-x-2

f^-1 (x)=

Answer 1

To find the inverse function \( f^{-1}(x) \) of the function \( f(x) = -x - 2 \), 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 \( y \):**
\[
x + 2 = -y
\]
\[
-y = x + 2
\]
\[
y = -x - 2
\]

4. **Replace \( y \) with \( f^{-1}(x) \):**
\[
f^{-1}(x) = -x - 2
\]

Thus, the inverse function is:
\[
f^{-1}(x) = -x - 2
\]

This is already in slope-intercept form \( mx + b \), where \( m = -1 \) and \( b = -2 \).