SOLUTION: f(x) = 3x-5 / x+2 f ^ -1 (x) = a) 2x+5 / x-3 b) -2x-5 / x-3 c) -2x-5 / x+5 d) 2x+3 / x-5 e) None of these

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: f(x) = 3x-5 / x+2 f ^ -1 (x) = a) 2x+5 / x-3 b) -2x-5 / x-3 c) -2x-5 / x+5 d) 2x+3 / x-5 e) None of these      Log On


   

Question 121733: f(x) = 3x-5 / x+2 f ^ -1 (x) =

a) 2x+5 / x-3
b) -2x-5 / x-3
c) -2x-5 / x+5
d) 2x+3 / x-5
e) None of these
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1

f%28x%29=%283x-5%29%2F%28x%2B2%29 Start with the given function


x=%283f%28x%29-5%29%2F%28f%28x%29%2B2%29 In order to find the inverse function, replace every x with f(x) and vice versa.

So the goal is to solve for f(x)


x%28f%28x%29%2B2%29=3f%28x%29-5 Multiply both sides by f%28x%29%2B2


xf%28x%29%2B2x=3f%28x%29-5 Distribute


xf%28x%29%2B2x-3f%28x%29=-5 Subtract 3f(x) from both sides


xf%28x%29-3f%28x%29=-5-2x Subtract 2x from both sides


xf%28x%29-3f%28x%29=-2x-5 Rearrange the terms


f%28x%29%28x-3%29=-2x-5 Factor out f(x)


f%28x%29=%28-2x-5%29%2F%28x-3%29 Divide both sides by x-3 to isolate f(x)



----------------------

So the inverse function is


f%5E%28-1%29%28x%29=%28-2x-5%29%2F%28x-3%29




So the answer is B)