SOLUTION: the function f(x)=(5x/x+7) is one to one find the inverse of f and the range of f using the inverse.

Algebra ->  Functions -> SOLUTION: the function f(x)=(5x/x+7) is one to one find the inverse of f and the range of f using the inverse.      Log On


   

Question 381187: the function f(x)=(5x/x+7) is one to one find the inverse of f and the range of f using the inverse.
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
from f(x)=5x/(x+7), we shall have x<>-7

let write f(x)=y, then y*(x+7)=5x=yx+7y

x(5-y)=7y => y = 7y/(5-y), hence y should be different from 5

Check : x(f(x))=7*5x/(x+7)/(5-5x/(x+7))=35x/(x+7)*(x+7)/(5x+35-5x)

=35x/35=x