document.write( "Question 1027568: Let f(x) an always positive function such that du/dx < 0 for all real numbers.
\n" ); document.write( "A) Let h(x) = [f(x)]^2. For what values of x will h(x) be increasing.
\n" ); document.write( "B) Let j(x) = f(f(x)). For what values of x will j(x) be increasing.
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Algebra.Com's Answer #642792 by robertb(5830)\"\" \"About 
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Let \"df%2Fdx+%3C+0\"\r
\n" ); document.write( "\n" ); document.write( "A) \"h%28x%29+=+%28f%28x%29%29%5E2\" ==> h'(x) = 2f(x)f'(x) < 0, because f(x) > 0 always and f'(x) < for all real numbers x.
\n" ); document.write( "Thus h(x) is decreasing for all real numbers x. Nowhere will it be increasing.\r
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\n" ); document.write( "\n" ); document.write( "B) j(x) = f(f(x)) = (fof)(x) ==> j'(x) = \"%28df%28f%28x%29%29%2Fdf%28x%29%29%2A%28df%28x%29%2Fdx%29\".
\n" ); document.write( "Now the domain of fof is a subset of the domain of f(x), hence by hypothesis, \"df%28f%28x%29%29%2Fdf%28x%29+%3C+0\". Also \"df%28x%29%2Fdx%3C0\" again by hypothesis.
\n" ); document.write( "==> j'(x) > 0, and so j(x) will always be increasing in the domain of (fof)(x).
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