Posted by **lilly** on Wednesday, March 27, 2013 at 1:15am.

The function f(x)=2x+8/3x-7 is one to one. Find its inverse, and check your answer.

f^-1(x)=

I haven't one clue how to do this...help me pleaaaase someone!

- math -
**Reiny**, Wednesday, March 27, 2013 at 7:46am
let y = (2x+8)/(3x-7) , notice the brackets are essential

step1: interchange the x and y variables to form the initial inverse.

x = (2y+8)/(3y-7)

step: solve this new equation for y

3xy - 7x = 2y+8

3xy - 2y = 7x + 8

y(3x - 2) = (7x + 8)

y = (7x + 8)/(3x - 2)

f^-1 (x) = (7x + 8)/(3x - 2)

test with some value of x, say x = 3

f(3) = 14/2 = 7

f^-1 (7) = should get 3 back ..

= (49+8)/(21-2) = 57/19 = 3 , looks ok

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