Question

How do you find the inverse of `f(x) =( -2x)/(-7-x)`?

Answer 1

`f^-1 (x)= (-7x)/(-2-x)`

Explanation:

First, change the term `f(x)` to `y`

Then, switch the x and y values. You should get
`x=(-2y)/(-7-y)`

Next solve for Y
-multiply x on the left side by `(-7-y)` to get rid of the denominator, you should get
`-7x-yx=-2y`

• add `yx` to both sides in order to get all the Ys on the same side
  -`7x=-2y+yx`

• factor out the y value from the right side
  -`7x=y(-2+x)`

• divide both sides by `(-2+x)`
  `(-7x)/(-2-x)=y`

Lastly change the term `y` to `f^-1 (x)` [f inverse of x]
`f^-1 (x)= (-7x)/(-2-x)`