Posted by **Millers** on Monday, October 14, 2013 at 3:06pm.

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

- Calculus -
**Reiny**, Monday, October 14, 2013 at 3:29pm
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.

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