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Prove that f(x)=x+3/2 and g(x)=2x-3 are inverses
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Let <em>X</em> be a random number selected from the interval. Then the probability density for the random variable <em>X</em> is
8 and 10 are the only even integers that fit the given criterion (6 is more than 0.25 away from 6.35), so that we're looking to compute
P(|<em>X</em> - 8| < 0.25) + P(|<em>X</em> - 10| < 0.25)
… = P(7.75 < <em>X</em> < 8.25) + P(9.75 < <em>X</em> < 10.25)
… = P(7.75 < <em>X</em> < 8.25) + P(9.75 < <em>X</em> < 10)
(since P(<em>X</em> > 10) = 0)
… = 0.2740 (8.25 - 7.75) + 0.2740 (10 - 9.75)
… = 0.2055