SOLUTION: Functions f and g are defined by f : x tends to x/(x-3) , x not equals 3, g : x tends to 3x+5. Find the value of x for which (f . g )^-1 (x) = 5/3.

Algebra ->  Finance -> SOLUTION: Functions f and g are defined by f : x tends to x/(x-3) , x not equals 3, g : x tends to 3x+5. Find the value of x for which (f . g )^-1 (x) = 5/3.      Log On


   



Question 1095376: Functions f and g are defined by f : x tends to
x/(x-3) , x not equals 3, g : x tends to 3x+5. Find the value of x for which (f . g )^-1 (x) = 5/3.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

I will assume that by "(f.g)^-1(x)" you mean the inverse of the composition of functions f and g; that is,
%28%28f%28g%28x%29%29%29%5E-1%29

In that case, the problem is asking you to find the input value x for which
f%28g%28x%29%29+=+5%2F3

Then
f%28g%28x%29%29+=+%283x%2B5%29%2F%28%283x%2B5%29-3%29+=+%283x%2B5%29%2F%283x%2B2%29
so
%283x%2B5%29%2F%283x%2B2%29+=+5%2F3
9x%2B15+=+15x%2B10
5+=+6x
x+=+5%2F6

Check:
g%285%2F6%29+=+3%285%2F6%29%2B5+=+5%2F2%2B5+=+15%2F2