- #1
terryds
- 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