find a formula for the inverse?

Question

find a formula for the inverse of the function
f(x)=

9x-1
_____

7x+9

Answer 1

All you have to do is change the x for y's and then solve for y.
Imagine y instead of f(x). (This is the first step!)
Now you have
x=(9y-1)/(7y+9)
Multiply both sides by (7y+9)
x(7y+9) = 9x-1
7xy+9x = 9x - 1 Subtract 9x from both sides.
9xy = -1
Divide by 9x
y = -1 / 9x
And that is your inverse. Plug it in a graphing calculator and you can see that they're perpendicular to each other, that means they're inverses.

Edit; I graphed them, and maybe I did something wrong with my algebra, but at least I showed you the steps.

Answer 2

is that 9x-1 divided by 7x+9 or are they two different questions? Either way all you need to do is take y=9x-1 and switch the x and y. Then solve for y. like y=9x-1 .... x=9y-1..... x+1=9y.... y= x=1 divided by 9... i hope that helps... is that what you meant?

Answer 3

I wonder whether you have one fractional function or two individual functions i will find the inverse of both cases.

Case 1. One Fractional function.
Inverse=
9x+1
--------- <---fraction bar
-7x+9

Case 2. Two different functions.

Inverse of first:x/9+1/9

Inverse of second:x/7-9/7

Answer 4

y=9x - 1

Recall: f^-1(x) = {(y,x) | such that y = f(x)}

So: x=9y-1 ==> y=(x+1)/9 = f^-1(x)

Do the same for y=7x+9

Answer 5

enable g(x) = (x-5)^3 = y y = (x-5)^3 => y^(a million/3) = x-5 => { y^(a million/3) } + 5 = x => x = 5 + y^(a million/3) ----------(a million) as g(x) = y x = g inverse y = 5 + y^(a million/3) considering the fact that from (a million) g inverse y = 5 + y^(a million/3) g inverse x = 5 + x^(a million/3) Have a advantageous day......

Answer 6

y = (9x-1)/(7x+9)
y(7x+9y)= 9x-1
7xy +9y^2 = 9x - 1
9y^2+1= 9x -7xy = (9-7y)x
x = (9y^2 +1)/(9-7y)