Inverse of the function?

Question

the problem is f(x)= x-5 / x+2

this is what i did and where i got stuck:

x = y-5 / y+2
x (y+2) = y-5 (cross multiplication)
x (y+2)+5 = y
x+5 = y / y+2 (i am pretty sure this last step i made is incorrect)

any help on how to correct/finish this?

Answer 1

you got the first two steps correct.

So when you get to

x(y+2)+5 = y,

you need to multiply (y+2) by x....You want to get y on its own side

xy+2x + 5 = y ; subtract both sides by xy

xy + 2x + 5 -xy = y-xy

2x +5 = y-xy ; factor out the y from the right side

2x+5 = y(1-x) ; divide both sides by (1-x)

(2x+5)/(1-x) = y

f-1(x) = (2x+5)/(1-x)

Answer 2

x = y-5
=> x(y+2) = y-5
=> xy + 2x = y-5
=> 2x + 5 = y - yx
=> y(1-x) = 2x + 5
=> y = 2x+5/1-x

Answer 3

x = y-5 / y+2
x (y+2) = y-5 (cross multiplication)
x (y+2)+5 = y
x+5 = y / y+2 (i am pretty sure this last step i made is incorrect

x(y+2)+5=y
xy+2x=y-5
x(y+2)=y-5
x=y-5/y+2

or xy+2x=y-5
xy+2x+5=y
y=xy+2x+5
y-xy=2x+5
y(1-x)=2x+5
y=2x+5/1-x

Answer 4

Yeh, you should get:
x(y+2) = xy+2x

xy+2x + 5 = y
2x + 5 = y - xy = y(1-x)
(2x+5)/(1-x) = y