document.write( "Question 814799: (f of g)(4) (g of f)(2) (f of f)(1)\r
\n" ); document.write( "\n" ); document.write( "f(x)=4x^2-3
\n" ); document.write( "g(x)=3-1/2x^2\r
\n" ); document.write( "\n" ); document.write( "I've been trying to solve this equation and i have spent about two hours on it. I think my problem might just be the fraction part. \n" ); document.write( "
Algebra.Com's Answer #490745 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"f%28x%29=4x%5E2-3\"
\n" ); document.write( "Is \"g%28x%29=3-%281%2F2%29x%5E2\" or \"g%28x%29=3-1%2F2x%5E2\"? If it is the first one, then use parentheses to show that the \"x%5E2\" is not in the denominator: g(x)=3-(1/2)x^2. I am going to assume that the first one is correct.

\n" ); document.write( "(f of g)(x) means f(g(x)):
\n" ); document.write( "(f of g)(x) = f(g(x))
\n" ); document.write( "(f of g)(x) = \"f%283-%281%2F2%29x%5E2%29\"
\n" ); document.write( "(f of g)(x) = \"4%283-%281%2F2%29x%5E2%29%5E2-3\"
\n" ); document.write( "Now we simplify. To square g(x) we can use FOIL or the \"%28a-b%29%5E2+=+a%5E2-2ab_b%5E2\" pattern. I prefer to use the pattern:
\n" ); document.write( "(f of g)(x) = \"4%28%283%29%5E2-2%283%29%28%281%2F2%29x%5E2%29%2B+%28%281%2F2%29x%5E2%29%5E2%29-3\"
\n" ); document.write( "Simplifying...
\n" ); document.write( "(f of g)(x) = \"4%289-3x%5E2%2B+%281%2F4%29x%5E4%29-3\"
\n" ); document.write( "Multiply by 4 using the Distributive Property:
\n" ); document.write( "(f of g)(x) = \"36-12x%5E2%2B+x%5E4-3\"
\n" ); document.write( "Re-arranging the terms and adding the constant terms:
\n" ); document.write( "(f of g)(x) = \"x%5E4-12x%5E2%2B+33\"
\n" ); document.write( "(f of g)(4) = \"%284%29%5E4-12%284%29%5E2%2B+33\"
\n" ); document.write( "Simplifying:
\n" ); document.write( "(f of g)(4) = \"256-12%2816%29%2B+33\"
\n" ); document.write( "(f of g)(4) = \"256-192%2B+33\"
\n" ); document.write( "(f of g)(4) = 97

\n" ); document.write( "(g of f(x) = g(f(x))
\n" ); document.write( "(g of f(x) = \"g%284x%5E2-3%29\"
\n" ); document.write( "(g of f(x) = \"3-%281%2F2%29%284x%5E2-3%29%5E2\"
\n" ); document.write( "Using the pattern again:
\n" ); document.write( "(g of f(x) = \"3-%281%2F2%29%28%284x%5E2%29%5E2-2%284x%5E2%29%283%29%2B%283%29%5E2%29\"
\n" ); document.write( "Simplifying...
\n" ); document.write( "(g of f(x) = \"3-%281%2F2%29%2816x%5E4-24x%5E2%2B9%29\"
\n" ); document.write( "Distributing the 1/2:
\n" ); document.write( "(g of f(x) = \"3-%288x%5E4-12x%5E2%2B9%2F2%29\"
\n" ); document.write( "Subtracting:
\n" ); document.write( "(g of f(x) = \"3-8x%5E4%2B12x%5E2-9%2F2%29\"
\n" ); document.write( "Simplifying...
\n" ); document.write( "(g of f(x) = \"6%2F2-8x%5E4%2B12x%5E2-9%2F2%29\"
\n" ); document.write( "(g of f(x) = \"-8x%5E4%2B12x%5E2-3%2F2%29\"
\n" ); document.write( "(g of f(2) = \"-8%282%29%5E4%2B12%282%29%5E2-3%2F2%29\"
\n" ); document.write( "Simplifying...
\n" ); document.write( "(g of f(2) = \"-8%2816%29%2B12%284%29-3%2F2%29\"
\n" ); document.write( "(g of f(2) = \"-128%2B48-3%2F2%29\"
\n" ); document.write( "(g of f(2) = \"-80-3%2F2%29\"
\n" ); document.write( "(g of f(2) = \"-160%2F2-3%2F2%29\"
\n" ); document.write( "(g of f(2) = \"-163%2F2%29\"

\n" ); document.write( "I'll leave (f of f)(1) to you. \n" ); document.write( "
\n" );