document.write( "Question 56064: If f(x) = 2x + 3 and g(x) = (x - 3)/2, what is the value of f[g(-5)]? \n" ); document.write( "
Algebra.Com's Answer #38019 by Edwin McCravy(20056)\"\" \"About 
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If f(x) = 2x + 3 and g(x) = (x - 3)/2, \r\n" );
document.write( "what is the value of f[g(-5)]? \r\n" );
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document.write( "f[g(-5)] means substitute -5 for x in the right side of g(x), \r\n" );
document.write( "simplify, then substitute what you get for x in the right \r\n" );
document.write( "side of f(x), then simplify.\r\n" );
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document.write( "It's a \"double substitution\".\r\n" );
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document.write( "To find f[g(-5)], work it from the inside out.\r\n" );
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document.write( "In f[g(-5)], do only the inside part first.\r\n" );
document.write( "In this case the inside part if the red part g(-5)\r\n" );
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document.write( "g(-5) means to substitute -5 for x in \r\n" );
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document.write( "g(x) = (x - 3)/2\r\n" );
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document.write( "So we take out the x's and we have\r\n" );
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document.write( "g(  ) = (   - 3)/2\r\n" );
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document.write( "Now we put -5's where we took out the x's, and we now \r\n" );
document.write( "have\r\n" );
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document.write( "g(-5) = (-5 - 3)/2\r\n" );
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document.write( "Then we simplify:\r\n" );
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document.write( "g(-5) = (-8)/2\r\n" );
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document.write( "g(-5) = -4\r\n" );
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document.write( "Now we have the g(-5)] \r\n" );
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document.write( "f[g(-5)]  \r\n" );
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document.write( "means to substitute g(-5) for x in \r\n" );
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document.write( "f[x] = 2x + 3\r\n" );
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document.write( "So we take out the x's and we have\r\n" );
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document.write( "f[     ] = 2[     ] + 3\r\n" );
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document.write( "Now we put g(-5)'s where we took out the x's, and we \r\n" );
document.write( "now have\r\n" );
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document.write( "f[g(-5)] = 2[g(-5)] + 3\r\n" );
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document.write( "But we have now found that g(-5) = -4, we can put \r\n" );
document.write( "that in place of the g(-5)'s and we get\r\n" );
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document.write( "f[g(-5)] = f[-4]\r\n" );
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document.write( "But then\r\n" );
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document.write( "f(-4) means to substitute -4 for x in\r\n" );
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document.write( "f(x) = 2x + 3\r\n" );
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document.write( "so \r\n" );
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document.write( "f(-4) = 2(-4) + 3\r\n" );
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document.write( "then we simplify  \r\n" );
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document.write( "f(-4) = -8 + 3\r\n" );
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document.write( "f(-4) = -5\r\n" );
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document.write( "So\r\n" );
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document.write( "f[g(-5)] = f(-4) = -5\r\n" );
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document.write( "Edwin
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