Better Students Ask More Questions.
find the equation of the inverse function for the following function f(x)=6/x+7
3 Answers | add yours
High School Teacher
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:
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).
Posted by embizze on June 3, 2013 at 6:38 PM (Answer #1)
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)`
Posted by ericmilamattim on June 3, 2013 at 6:38 PM (Answer #2)
1 Reply | Hide Replies ▲
Join to answer this question
Join a community of thousands of dedicated teachers and students.