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
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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) (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 ) = g(g^{-1}(x)) = x)
for all x, if it exists.
To solve, let )
and solve for x:
)
Replace x with g^{-1} x and y with x:
 = \frac{1}{2}(1-x))
As a check, ) = g(\frac{1}{2}(1-x)) = 1 - 2(\frac{1}{2}(1-x) = x)
and ) = g^{-1}(1-2x) = \frac{1}{2}(1 - (1-2x)) = x)
.
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