# Question #8e6ef

To find the inverse of any function, you can follow these general steps:

1) Change the function notation f(x), g(x) etc. to y =
2) Interchange x and y : that is, swap the x's and the y's
3) Isolate for y
4) Put inverse back into function notation using ${f}^{- 1} \left(x\right)$ to represent the inverse

#### Explanation:

In your example you have $h \left(x\right) = \frac{4}{- x - 3} + 1$:

1) Change the function notation f(x), g(x) etc. to y = :

Simple: Let h(x) = y and thus,

$y = \frac{4}{- x - 3} + 1$

2) Interchange x and y : that is, swap the x's and the y's:

$x = \frac{4}{- y - 3} + 1$

3) Isolate for y :

Subtract 1 from both sides:

$x - 1 = \frac{4}{- y - 3}$

Multiply by (-y-3) on both sides to get y on top and on the left:

$\left(x - 1\right) \left(- y - 3\right) = 4$

Divide by (x-1) on both sides:

$- y - 3 = \frac{4}{x - 1}$

-y = 4/(x-1)+3

Now, divide by -1 on both sides to get:

$y = - \frac{4}{x - 1} + 3$

4) Put inverse back into function notation using ${f}^{- 1} \left(x\right)$ to represent the inverse :

$h ' \left(x\right) = - \frac{4}{x - 1} + 3$

And that's your inverse! Hopefully things were clear! Should you have any questions, feel free to ask! :)