Question

Find the inverse of f(x) = (5x-4)/(x+4)

Answer 1

I want to see if I'm on the right track...
y = 5x-4/x+4
(y+4)*x = 5y-4
xy + 4x - 4x = 5y - 4
xy = 5y-4-4x

Answer 2

that is correct so far

Answer 3

now get the 5y to the other side
and factor out the y

Answer 4

xy-5y=-4-4x

Answer 5

5(y-x)=-4-4x

Answer 6

Oh I factored out the wrong thing

Answer 7

y(-5+x)=-4-4x

Answer 8

yes
then divide (-5+x)

Answer 9

y = -4-4x/-5+x

Answer 10

that is correct

Answer 11

wow that is a lot of steps for this one

Answer 12

could I have taken a shortcut?

Answer 13

I don't see any short cuts...

Answer 14

you could, however, factor out and cancel out some negatives

Answer 15

can you give me an example?

Answer 16

I got f^-1(x) = 4(x+1) / (5-x)

Answer 17

That is a nicer solution... mine is (-4-4x)/(-5+x) and it was correct

Answer 18

yes it was

Answer 19

now I wonder how you got your answer

Answer 20

........
(y+4)*x = 5y-4
xy + 4x = 5y - 4
-xy -xy
4x = 5y - xy -4
+4 +4
4x + 4 = 5y - xy
4x + 4 = y(5-x)
y = (4x+4)/(5-x)

Answer 21

Oh so you subtracted xy first and I subtracted 4x