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If f(x) = 4^x/(4^x + 2), then the value of f(x) + f(1 - x) is:

1. 0
2. -1
3. 1
4. 4

Correct answer: 1

Solution

f(1-x) = 4^(1-x)/(4^(1-x)+2) = (4/4^x)/((4/4^x)+2). Multiply top and bottom by 4^x: = 4/(4 + 2*4^x) = 2/(2 + 4^x). Then f(x) + f(1-x) = 4^x/(4^x+2) + 2/(4^x+2) = (4^x+2)/(4^x+2) = 1.

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