Question

find the inverse of the function$g(x) = \frac{4}{ - x - 3 } - 2$

Answer 1

Given:

The function is,

$\begin{gathered} g(x)=\frac{4}{-x-3}-2 \\ y=\frac{4}{-x-3}-2 \end{gathered}$

The objective is to find the inverse of the function.

To find the inverse of a function, interchange the variables x and y and solve for y.

Then, the above equation can be represented as,

$\begin{gathered} x=\frac{4}{-y-3}-2 \\ x+2=\frac{4}{-y-3} \\ -y-3=\frac{4}{x+2} \end{gathered}$