[tex]c)f^{-1}(x)=-\frac{x}{5}-\frac{8}{5}[/tex]
Explanation[tex]f(x)=-8-5x[/tex]
An inverse function essentially undoes the effects of the original function,it is given by
[tex]f^{-1}(x)\rightarrow inverse\text{ of f(x)}[/tex]
to find the inverse of a function do:
Step 1
strick a "y" in f(x)
[tex]\begin{gathered} f(x)=-8-5x \\ y=-8-5x \end{gathered}[/tex]
Step 2
swap x and y
[tex]\begin{gathered} y=-8-5x \\ y=-8-5x\rightarrow x=-8-5y \\ x=-8-5y \end{gathered}[/tex]
Step 3
solve for y and write in the inverse notation
[tex]\begin{gathered} x=-8-5y \\ \text{add 8 in both sides} \\ x+8=-8-5y+8 \\ x+8=-5y \\ \text{divide both sides by -5} \\ \frac{x+8}{-5}=\frac{-5y}{-5} \\ -\frac{x}{5}-\frac{8}{5}=y \\ y=-\frac{x}{5}-\frac{8}{5} \end{gathered}[/tex]
use the inverse notation
[tex]\begin{gathered} y=-\frac{x}{5}-\frac{8}{5} \\ f^{-1}(x)=-\frac{x}{5}-\frac{8}{5} \end{gathered}[/tex]
so, the answer is
[tex]c)f^{-1}(x)=-\frac{x}{5}-\frac{8}{5}[/tex]
I hope this helps you
