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

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clevedog | eNotes Newbie

Posted June 3, 2013 at 6:16 PM via web

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find the equation of the inverse function for the following function

f(x)=6/x+7

 

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 3, 2013 at 6:38 PM (Answer #1)

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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`

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

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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).

 

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ericmilamattim | Honors

Posted June 3, 2013 at 6:38 PM (Answer #2)

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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)`

 

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ericmilamattim | Honors

Posted June 3, 2013 at 6:45 PM (Reply #1)

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my solution is for f(x)=`(6/x)+7`

 

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ericmilamattim | Honors

Posted June 3, 2013 at 6:43 PM (Answer #3)

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Additional Info:

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

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