Find a formula for the inverse of the function. f(x) = (1 + 9x) / (8 - 4x)

Answer 1

let y = (1+9x)/(8-4x)
for inverse, interchange the x and y variables

x = (1+9y)/(8-4y)
now solve this for y .....

8x - 4xy = 1 + 9y
8x - 1 = 9y + 4xy
y(9+4x) = 8x-1

y = (8x-1)/(9+4x)
or
f^-1 (x) = (8x-1)/(9+4x)

check with some arbitrary x
say x = -1
f(-1) = (1-9)/(8+4) = -8/12 = -2/3
f^-1 (-2/3)
= (8(-2/3) - 1)/(9 + 4(-2/3))
= (-19/3) / (19/3)
= -1 , as expected
"more than likely" my answer is correct.