(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let

f(x) = (1/2+x) log [(1+x)/x] + (3/2-x) log [(1-x)/(2-x)]

where log is natural logarithm and 0 < x <= 1/2. Show that f(x) >= 0 for all x.

2. Relevant equations

The only inequality that I can think of is the log sum inequality:

http://en.wikipedia.org/wiki/Log_sum_inequality

3. The attempt at a solution

I try to plot f (see figure), and it seems that the statement is correct. In fact, the figure suggests that f is decreasing and equals 0 at x = 1/2. However, I can't figure out an analytical proof of this.

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# Homework Help: Algebra: proving an inequality

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