SOLUTION: Let {{{h(x)= 2/(3x+2)}}} and let {{{g(x)= (2-2x)/3x}}}. Show that these two functions are inverses.

Algebra ->  Inverses -> SOLUTION: Let {{{h(x)= 2/(3x+2)}}} and let {{{g(x)= (2-2x)/3x}}}. Show that these two functions are inverses.       Log On


   

Question 1006927: Let h%28x%29=+2%2F%283x%2B2%29 and let g%28x%29=+%282-2x%29%2F3x. Show that these two functions are inverses.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Switch to x-y format using h(x) as the function.
y=2%2F%283x%2B2%29
Interchange x and y and solve for the new y.
x=2%2F%283y%2B2%29
x%283y%2B2%29=2
3xy%2B2x=2
3xy=2-2x
y=%282-2x%29%2F3x
This new y is the inverse of the original y.
Since it equals g, then f and g are inverses.