Question

I need some help on question 4 I would appreciate it:0

Answer 1

`c)f^(-1)(x)=-(x)/(5)-(8)/(5)`

Step-by-step explanation
`f(x)=-8-5x`

An inverse function essentially undoes the effects of the original function,it is given by

`f^(-1)(x)\rightarrow inverse\text{ of f(x)}`

to find the inverse of a function do:

Step 1

strick a "y" in f(x)

`\begin{gathered} f(x)=-8-5x \\ y=-8-5x \end{gathered}`

Step 2

swap x and y

`\begin{gathered} y=-8-5x \\ y=-8-5x\rightarrow x=-8-5y \\ x=-8-5y \end{gathered}`

Step 3

solve for y and write in the inverse notation

`\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} \\ (x+8)/(-5)=(-5y)/(-5) \\ -(x)/(5)-(8)/(5)=y \\ y=-(x)/(5)-(8)/(5) \end{gathered}`

use the inverse notation

`\begin{gathered} y=-(x)/(5)-(8)/(5) \\ f^(-1)(x)=-(x)/(5)-(8)/(5) \end{gathered}`

so, the answer is

`c)f^(-1)(x)=-(x)/(5)-(8)/(5)`

I hope this helps you