SOLUTION: The function g is defined by g(x) = 1-2x, where x belongs to the real numbers. Find the function g^(-1) The answer given in the textbook is: x = 1/2(1-x) I thought

Algebra ->  Functions -> SOLUTION: The function g is defined by g(x) = 1-2x, where x belongs to the real numbers. Find the function g^(-1) The answer given in the textbook is: x = 1/2(1-x) I thought      Log On


   



Question 941088: The function g is defined by g(x) = 1-2x, where x belongs to the real numbers.

Find the function
g^(-1)
The answer given in the textbook is:
x = 1/2(1-x)
I thought the answer would be 1 / (1-2x) but then how would that get to the answer given in the textbook?
Trying to work backwards from the answer 1/2(1-x) would become 1/2 - 1/2x but I can't see how that came about.
Any help given would be appreciated. Thanks.

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
In this context, is not the reciprocal of g(x). It is the function such that for all x, if it exists.


To solve, let and solve for x:







Replace x with g^{-1} x and y with x:



As a check, and .