SOLUTION: Please show work: The function {{{f(x)= 2x/(x+5)}}} is a one-to-one. find its inverse and check the answer. (note: the {{{2x/(x+5)}}} is all in fraction form 2x is the numerator a

Algebra ->  Functions -> SOLUTION: Please show work: The function {{{f(x)= 2x/(x+5)}}} is a one-to-one. find its inverse and check the answer. (note: the {{{2x/(x+5)}}} is all in fraction form 2x is the numerator a      Log On


   

Question 714843: Please show work: The function f%28x%29=+2x%2F%28x%2B5%29 is a one-to-one. find its inverse and check the answer.
(note: the 2x%2F%28x%2B5%29 is all in fraction form 2x is the numerator and x+5 is the denominator)
note: grouping symbols added.
thanks for your help!
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is not the exact formal way to look for the inverse but is usually easy, fast.

From given f%28x%29=%282x%29%2F%28x%2B5%29, switch places of x and f(x), but call f(x) something else.

y=(2x)/(x+5), from that make, x=2y%2F%28y%2B5%29 and try to solve for y.
x%28y%2B5%29=2y
xy%2B5x=2y
xy-2y=-5x
y%28x-2%29=-5
highlight%28y=%28-5%29%2F%28x-2%29%29, but we should maybe call this, like g(x) as
g%28x%29=%28-5%29%2F%28x-2%29 and say that g(x) and f(x) are inverses.