Calculus
posted by Millers on .
Find a formula for the inverse of the function. f(x) = (1 + 9x) / (8  4x)

let y = (1+9x)/(84x)
for inverse, interchange the x and y variables
x = (1+9y)/(84y)
now solve this for y .....
8x  4xy = 1 + 9y
8x  1 = 9y + 4xy
y(9+4x) = 8x1
y = (8x1)/(9+4x)
or
f^1 (x) = (8x1)/(9+4x)
check with some arbitrary x
say x = 1
f(1) = (19)/(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.