# find the equation of the inverse function for the following function f(x)=6/x+7

embizze | Certified Educator

Find the inverse for `f(x)=6/(x+7)` :

`y=6/(x+7)`    Exchange x and y:

`x=6/(y+7)`   Now solve for y:

`y+7=6/x`

`y=6/x-7`

-------------------------

So `f^(-1)(x)=6/x-7`

-------------------------

The graphs should be reflections across the line y=x:

For f(x) we did the following to x: add 7 then reciprocate then multiply by 6

For the inverse we took x; divided by 6 `x/6` , reciprocated `6/x` , then subtracted 7 `6/x-7` -- taking the inverse actions or "undoing" f(x).

ericmilamattim | Student

***My solution is for f(x) = (6/x)+7

ericmilamattim | Student

The inverse of any function y= f(x) is `f^-1(x)`

all we need to do is to interchange x and y and express it in y form.

example:

y=6/x+7

interchange the position of x and y

x = 6/y + 7

multiply this by y to get rid of the denominator

xy = 6 + 7y

transpose 7y to the left

xy-7y = 6

factor by y

y(x -7) = 6

y=`6/(x-7)`

` `

replace y by `f^-1(x)`

`f^-1(x) = 6/(x-7)`