document.write( "Question 787140: How do I solve these kind of questions:
\n" ); document.write( "1) f(x)=2x+3, g(x)=x^2-1, find (fog)(3)
\n" ); document.write( "2) f(x)=3x-2, g(x)=x+2 / 3, find (fog)(x)
\n" ); document.write( "3) f(x)= root x, g(x)=-x^2-2, find (fog)(x)
\n" ); document.write( "4) f(x)=x^2-1, g(x)=x^2+1, find (fog)(x) - (gof)(x)\r
\n" ); document.write( "\n" ); document.write( "Thank you. \n" ); document.write( "
Algebra.Com's Answer #478125 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
How do I solve these kind of questions:
\n" ); document.write( "1) f(x)=2x+3, g(x)=x²-1, find (f∘g)(3)
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document.write( "(f∘g)(3) = f(g(3))\r\n" );
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document.write( "Find g(3) by substituting x=3 in g(x)\r\n" );
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document.write( "g(x)=x²-1\r\n" );
document.write( "g(3)=3²-1\r\n" );
document.write( "g(3)=9-1\r\n" );
document.write( "g(3)=8\r\n" );
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document.write( "f∘g(3) = f(g(3)) = f(8)\r\n" );
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document.write( "find f(8) by substituting x=8 in f(x):\r\n" );
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document.write( "f(x)=2x+3\r\n" );
document.write( "f(8)=2(8)+3\r\n" );
document.write( "f(8)=16+3\r\n" );
document.write( "f(8)=19\r\n" );
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document.write( "So f∘g(3) = 19\r\n" );
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document.write( "-------------------------\r\n" );
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\n" ); document.write( "2) f(x)=3x-2, g(x)=\"%28x%2B2%29%2F3\", find (f∘g)(x)
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document.write( "(f∘g)(x) = f(g(x)) = f\"%28%28x%2B2%29%2F3%29\"\r\n" );
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document.write( "Find f\"%28%28x%2B2%29%2F3%29\" by replacing x by\r\n" );
document.write( "\"%28x%2B2%29%2F3\" in f(x)\r\n" );
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document.write( "f(x)=3x-2\r\n" );
document.write( "f\"%28%28x%2B2%29%2F3%29\"=3\"%28%28x%2B2%29%2F3%29\"-2\r\n" );
document.write( "f\"%28%28x%2B2%29%2F3%29\"=(x+2)-2\r\n" );
document.write( "f\"%28%28x%2B2%29%2F3%29\"=x+2-2\r\n" );
document.write( "f\"%28%28x%2B2%29%2F3%29\"=x\r\n" );
document.write( "So\r\n" );
document.write( "(f∘g)(x) = x\r\n" );
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\n" ); document.write( "3) 
f(x) = √x
, g(x)=-x²-2, find (f∘g)(x)
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document.write( "(f∘g)(x) = f(g(x)) = f(-x²-1)\r\n" );
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document.write( "Find f(-x²-1) by replacing x by\r\n" );
document.write( "-x²-1 in f(x)\r\n" );
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document.write( "f(x) = √x\r\n" );
document.write( "f(-x²-1) = √-x²-1\r\n" );
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document.write( "So \r\n" );
document.write( "(f∘g)(x) = √-x²-1 \r\n" );
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document.write( "--------------------------\r\n" );
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\n" ); document.write( "4) f(x)=x²-1, g(x)=x²+1,
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document.write( "(f∘g)(x) - (g∘f)(x) =\r\n" );
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document.write( "f(g(x)) - g(f(x)) =\r\n" );
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document.write( "f(x²+1) - g(x²-1) =\r\n" );
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document.write( "[(x²+1)²-1] - [(x²-1)²+1] =\r\n" );
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document.write( "[x²+2x+1-1] - [x²-2x+1+1] =\r\n" );
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document.write( "[x²+2x] - [x²-2x+2] =\r\n" );
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document.write( "x²+2x-x²+2x-2 =\r\n" );
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document.write( "4x-2\r\n" );
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document.write( "Edwin
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