1. ## functions

f(x) = 2x+1
g(x) = 3x-5

find g^-1 of f^-1 of 2

2. Originally Posted by DINOCALC09
f(x) = 2x+1
g(x) = 3x-5

find g^-1 of f^-1 of 2
Let $g(x) = y_1 = 3x - 5$

for $g^{-1}$ switch $x$ and $y$ and solve for $y$

so, $x = 3y_1 - 5$

$y_1 = \frac {x + 5}3$

thus, $g^{-1}(x) = \frac {x + 5}3$

similarly, $f^{-1}(x) = \frac {x - 1}2$

now can you find $g^{-1} \circ f^{-1}(x) = g^{-1} \left( f^{-1} (x) \right)$?