#1 pre-calculus: Find inverse of f(x) = x/(9x - 7), etc

[greenblunts]

Consider the function
f(x)=x/(9x-7)
a) Find the inverse of f.
f^{-1}(x)=
(b) The domain of f is: 7/9 (i got that one)
(c) The domain of f^{-1} is:
(d) The range of f is:
(d) The range of f^{-1} is:

i cant for the life of me get x by itself on one side of the problem so i cant get the inverse of f. PLEASE HELP ME!

 

[steve_b]

Consider the function
f(x)=x/(9x-7)
a) Find the inverse of f.
f^{-1}(x)=

----------

y = x/(9x-7)

y(9x-7) = x

9xy - 7y = x

9xy - x = 7y

x(9y - 1) = 7y

x = 7y/(9y - 1)

Inverse fct:

y = 7x/(9x - 1)

---------------
(b) The domain of f is: 7/9 (i got that one)

The domain of f is all x except x = 7/9

Steve