- #1

- 392

- 13

## Homework Statement

If ##f(2x-1)= 6x + 15## and ##g(3x+1)=\frac{2x-1}{3x-5}##, then what is ##f^{-1}\circ g^{-1}(3)## ?

a) -2

b) -3

c) -4

d) -5

e) -6

## The Attempt at a Solution

I think the f inverse and g inverse is

##f^{-1}(6x+15)= 2x-1##

##g^{-1}(\frac{2x-1}{3x-5})=3x+1##

and,##f^{-1}\circ g^{-1}(3)=f^{-1}(g^{-1}(3))##

Then,

I equate ##\frac{2x-1}{3x-5}=3##

So, I get x = 2

So, ##g^{-1}(3)=3(2)+1=7##

Then, I equate ##6x+15=7##

And, I get x = 8/6 or 4/3

So, ##f^{-1}(7)=2(\frac{4}{3})-1=\frac{5}{3}## which does not appear in the options..

Please help me figure out what's wrong