posted by lilly on .
The function f(x)=2x+8/3x-7 is one to one. Find its inverse, and check your answer.
I haven't one clue how to do this...help me pleaaaase someone!
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