Question

Let f(x) = (3x - 7)/(x + 1. Find the inverse f^-1(x).

Once again, thank you so much for helping me!

Answer 1

let y = (3x - 7)/(x + 1)

for the inverse , exchange the x and y's
x = (3y-7)/(y+1)
now solve this for y ...

xy + x = 3y - 7
xy - 3y = -x - 7
y(x-3) = -x - 7
y = (-x - 7)/(x - 3) = (x+7)/(3-x)

<b>f^-1 (x) = (x+7)/(3-x)</b>

check:
f(1) = (3-7)/(2
= -2
f^-1 (-2) = (-2+7)/(3-(-2))
= 5/5 = 1
my answer is reasonable

Answer 2

Thank you Reiny for helping! I understand the problem now! :)