Question

If f(x)=1/9x-2, what us f^-1(x)

Answer 1

Step-by-step explanation:

The initial function is:

`f(x)=(1)/(9)x-2`

So, to find the inverse function f^(-1)(x), we first need to replace f(x) by y as:

`y=(1)/(9)x-2`

Then, we need to solve the equation for x as follows:

`\begin{gathered} y+2=(1)/(9)x-2+2 \\ y+2=(1)/(9)x \\ 9\cdot(y+2)=9\cdot(1)/(9)x \\ 9(y+2)=x \\ 9y+18=x \end{gathered}`

Now, we need to interchange x and y as:

`\begin{gathered} 9x+18=y \\ or \\ y=9x+18 \end{gathered}`