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The function f satisfies = .
for all x not equal to 1/2. Find f(2).
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The idea is to find x such that = 2
and then calculate f(2) using the given functional equation.
Below is an implementation of this idea in steps.
Step 1. We want to find x from equation
= 2.
Do all necessary transformations as follow
2x-1 = 2^2 = 4,
2x = 4 + 1 = 5,
x = 5/2.
Step 2. According to the functional equation,
= .
Substitute here x = 5/2. Remember that x is determined in a way that = 2.
Therefore, you will get
f(2) = = = .
ANSWER<. f(2) = .
At this point, the problem is solved completely.