Question

How to solve this problem step by step in depth. I have no idea how to solve this

Answer 1

`f^(-1)(x)=(-1)/(5)x-(4)/(5)`

Step-by-step explanation

The given function is

`f(x)=-5x-4`

Let y = f(x), this implies

`y=-5x-4`

Now, make x the subject of the formula

`\begin{gathered} y=-5x-4 \\ 5x=-y-4 \\ \text{To get x, we divide both sides by 5} \\ (5x)/(5)=(-y-4)/(5) \\ \\ x=(-y-4)/(5) \end{gathered}`

Since f(x) = y, then x = f⁻¹(y)

`\begin{gathered} f^(-)^(1)\mleft(y\mright)=(-y-4)/(5) \\ \therefore f^(-1)(x)=(-x-4)/(5) \end{gathered}`

The above inverse function can be rewritten as follows

`\begin{gathered} f^(-1)(x)=(-x)/(5)-(4)/(5) \\ f^(-1)(x)=(-1)/(5)x-(4)/(5) \end{gathered}`