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Algebra.Com's Answer #762557 by greenestamps(13200)![\"\"](\"/images/stars/stars-13.gif\")  You can put this solution on YOUR website! \n" ); document.write( "The given function performs 4 operations on the input value: \n" ); document.write( "(1) square it; \n" ); document.write( "(2) subtract 1; \n" ); document.write( "(3) take the square root; and \n" ); document.write( "(4) add 2 \n" ); document.write( "So you could write the function as the composition of 4 functions: \n" ); document.write( "p(x) = x^2 \n" ); document.write( "q(x) = x-1 \n" ); document.write( "r(x) = sqrt(x) \n" ); document.write( "s(x) = x+2 \n" ); document.write( "s(r(q(p(x)))) = s(r(q(x^2))) = s(r(x^2-1)) = s(sqrt(x^2-1)) = sqrt(x^2-1)+2 \n" ); document.write( "If you need to write the function as the composition of 3 functions, none of which is the identity, simply combine two of the four operations into one. So one possible answer is \n" ); document.write( "h(x) = x^2 \n" ); document.write( "g(x) = sqrt(x-1) \n" ); document.write( "f(x) = x+2 \n" ); document.write( "Then \n" ); document.write( "f(g(h(x))) = f(g(x^2)) = f(sqrt(x^2-1) = sqrt(x^2-1)+2 \n" ); document.write( "There are of course other possible answers.... \n" ); document.write( " |