document.write( "Question 1209326: Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if a(x) = 2x - 5 and b(x) = 4 + 7x - 3x^2. \n" ); document.write( "

Algebra.Com's Answer #848375 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "Let a(x) and b(x) be functions. Find (a o b)(3) - (b o a)(3)
\n" ); document.write( "if a(x) = 2x - 5 and b(x) = 4 + 7x - 3x^2.
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\n" ); document.write( "\n" ); document.write( "        They do not ask to express implicitly the composite functions.\r
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\n" ); document.write( "\n" ); document.write( "        Therefore, the shortest and the easiest way is to calculate the interior argument\r
\n" ); document.write( "\n" ); document.write( "        of the composite function, then calculate the values of the composite functions\r
\n" ); document.write( "\n" ); document.write( "        and then take their difference.\r
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document.write( "For (a o b)(3) = a(b(3)), we calculate first b(3) = 4 + 7*3 - 3*3^2 = -2.\r\n" );
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document.write( "Then we calculate  a(b(3)) = a(-2) = 2*(-2) - 5 = -9.\r\n" );
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document.write( "For (b o a)(3) = b(a(3)), we calculate first a(3) = 2*3 - 5 = 1.\r\n" );
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document.write( "Then we calculate  b(a(3)) = b(1) = 4 + 7*1 - 3*1^2 = 8.\r\n" );
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document.write( "Finally,  (a o b)(3) - (b o a)(3) = -9 - 8 = -17.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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