document.write( "Question 1027568: Let f(x) an always positive function such that du/dx < 0 for all real numbers.
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document.write( "A) Let h(x) = [f(x)]^2. For what values of x will h(x) be increasing.
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document.write( "B) Let j(x) = f(f(x)). For what values of x will j(x) be increasing. \n" );
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Algebra.Com's Answer #642792 by robertb(5830)![]() ![]() You can put this solution on YOUR website! Let \n" ); document.write( "\n" ); document.write( "A) \n" ); document.write( "Thus h(x) is decreasing for all real numbers x. Nowhere will it be increasing.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "B) j(x) = f(f(x)) = (fof)(x) ==> j'(x) = \n" ); document.write( "Now the domain of fof is a subset of the domain of f(x), hence by hypothesis, \n" ); document.write( "==> j'(x) > 0, and so j(x) will always be increasing in the domain of (fof)(x). \n" ); document.write( " |