SOLUTION: Let f(x) = 7x +5 / 2x - 5. Find f^-1(x).

Algebra ->  Functions -> SOLUTION: Let f(x) = 7x +5 / 2x - 5. Find f^-1(x).       Log On


   

Question 305939: Let f(x) = 7x +5 / 2x - 5. Find f^-1(x).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use x,y notation.
y=%287x%2B5%29%2F%282x-5%29
Now interchange the x's and y's and solve for y.
highlight%28+x%29=%287highlight%28+y%29%2B5%29%2F%282highlight%28+y%29-5%29
%282y-5%29x=7y%2B5
2yx-5x=7y%2B5
2yx-7y=5%2B5x
y%282x-7%29=5x%2B5
y=%285x%2B5%29%2F%282x-7%29%29
highlight_green%28f%5E%28-1%29%28x%29=%285x%2B5%29%2F%282x-7%29%29
This new y is the inverse of the original function.