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

3 Answers

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

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:




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's profile pic

ericmilamattim | (Level 1) Honors

Posted on

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.



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


` `

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

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


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