g(x) = y
y + 2 / y -1 = x
y + 2 = xy - x
y - xy = -x - 2 ... y (1 - x) = -x - 2 ... y = (x + 2) / (x - 1)
Let f(x) = x+2/x-1. Find a function g(x) so that f(g(x)) = x.
How do I solve this? I’m stuck on what to do.
Thank you!
2 answers
Well, that can only be true if g(x) is the inverse of f(x).
let y = f(x) = (x+2)/(x-1) , I assumed those brackets were needed
then the inverse would be
x = (y+2)/(y-1)
xy - x = y+2
xy - y = x+2
y(x - 1) = x + 2
y = (x + 2)/(x - 1)
g(x) = (x+2)/(x-1)
check:
let x = 7 , or any arbitrary number you want
g(7) = 9/6 = 3/2
f(3/2) = (3/2+2)/(3/2-1)
= (7/2) / (1/2)
= (7/2)(2/1) = 7
It is highly unlikely that I would have obtained that result had my g(x) answer been incorrect.
let y = f(x) = (x+2)/(x-1) , I assumed those brackets were needed
then the inverse would be
x = (y+2)/(y-1)
xy - x = y+2
xy - y = x+2
y(x - 1) = x + 2
y = (x + 2)/(x - 1)
g(x) = (x+2)/(x-1)
check:
let x = 7 , or any arbitrary number you want
g(7) = 9/6 = 3/2
f(3/2) = (3/2+2)/(3/2-1)
= (7/2) / (1/2)
= (7/2)(2/1) = 7
It is highly unlikely that I would have obtained that result had my g(x) answer been incorrect.
1 answer