Write a formula for f^-1 (x) if f(x) = (x+5)/(3x-4) and state the domain of F^-1

Answer 1

let y = (x+5)/(3x-4)
First step in finding the inverse is to interchange the x and y variables , so ...

inverse is: x = (y+5)/(3y-4)

2nd step: solve this new equation for y

cross-multiply
3xy - 4x = y+5
3xy -y = 4x+5
y(3x-1) = 4x+5
y = (4x+5)/(3x-1)

f^-1 (x) = (4x+5)/(3x-1) , domain is set of real numbers, x ≠ 1/3

check with some point
f(3) = 8/5

f^-1 (8/5) = (32/5 + 5)/(24/5 - 1)
= (57/5) / (19/5)
= 3