Question

Question #8e6ef

Answer 1

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)(x)` to represent the inverse **

Explanation:

In your example you have `h(x) = 4/(-x-3) + 1`:

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

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

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

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

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

3) ** Isolate for y **:

Subtract 1 from both sides:

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

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

`(x-1)(-y-3) = 4`

Divide by (x-1) on both sides:

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

Add 3 to both sides:

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

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

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

4) Put inverse back into function notation using `f^(-1)(x)` to represent the inverse :

`h'(x) = -4/(x-1)+3`

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