To find the inverse function of [tex]\( f(x) = -5x - 4 \)[/tex], we follow these steps:
1. Start with the function definition:
[tex]\[
y = -5x - 4
\][/tex]
2. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
- Add 4 to both sides:
[tex]\[
y + 4 = -5x
\][/tex]
- Divide both sides by -5:
[tex]\[
x = -\frac{y + 4}{5}
\][/tex]
Since dividing by -5 is the same as multiplying by [tex]\(-\frac{1}{5}\)[/tex], we get:
[tex]\[
x = -\frac{1}{5}(y + 4)
\][/tex]
3. Rewrite the equation to express [tex]\( x \)[/tex] as a function of [tex]\( y \)[/tex]:
[tex]\[
x = -\frac{1}{5} y - \frac{4}{5}
\][/tex]
4. Interchange [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to get the inverse function:
[tex]\[
f^{-1}(x) = -\frac{1}{5} x - \frac{4}{5}
\][/tex]
So, the correct inverse function is:
[tex]\[
f^{-1}(x) = -\frac{1}{5} x - \frac{4}{5}
\][/tex]
Thus, the answer is:
[tex]\[
f^{-1}(x) = -\frac{1}{5} x - \frac{4}{5}
\][/tex]
