SOLUTION: The function {{{ f(x)= (4x+7)/(9x-5) }}} is one to one. Find its inverse and check your answer. {{{ f^(-1)(x) }}} Thank you in advance

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The function {{{ f(x)= (4x+7)/(9x-5) }}} is one to one. Find its inverse and check your answer. {{{ f^(-1)(x) }}} Thank you in advance      Log On


   

Question 827031: The function ++f%28x%29=+%284x%2B7%29%2F%289x-5%29++ is one to one. Find its inverse and check your answer. ++f%5E%28-1%29%28x%29++
Thank you in advance
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
y = %284x%2B7%29%2F%289x-5%29
swap x and y and solve for y
x = %284y%2B7%29%2F%289y-5%29
x(9y-5) = 4y + 7
:
9xy - 5x = 4y + 7
:
9xy - 4y = 5x + 7
Factor out y
y(9x - 4) = 5x + 7
y = %28%285x%2B7%29%29%2F%28%289x-4%29%29
:
f%5E%28-1%29%28x%29 = %28%285x%2B7%29%29%2F%28%289x-4%29%29