What is f(0.5) equal to?
Consider the following for the next two (02) items that follow: Let a function f be defined on \mathbb{R}-\{0\} and 2f(x)+f\left(\frac{1}{x}\right)=x+3.
- A. \frac{1}{2}
- B. \frac{2}{3} ✓
- C. 1
- D. 2
Correct Answer: B. \frac{2}{3}
Explanation
Substitute x = \frac{1}{2} to get: 2f(\frac{1}{2}) + f(2) = \frac{7}{2}. Next, substitute x = 2 into the original equation to get: 2f(2) + f(\frac{1}{2}) = 5, meaning f(2) = \frac{5 - f(1/2)}{2}. Substitute this back into the first equation: 2f(\frac{1}{2}) + \frac{5 - f(1/2)}{2} = \frac{7}{2}. Multiplying by 2 gives 4f(\frac{1}{2}) + 5 - f(\frac{1}{2}) = 7 \implies 3f(\frac{1}{2}) = 2 \implies f(0.5) = \frac{2}{3}.
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