document.write( "Question 33362This question is from textbook College Algebra
\n" ); document.write( ": I need to find the functions (f o g), (g o f),(f o f), and (g o g) and their domains for:
\n" ); document.write( "34. f(x) = x^2, g(x) = sqrt(x-3)\r
\n" ); document.write( "\n" ); document.write( "38. f(x) = 1/sqrt(x), g(x) = x^2 - 4x\r
\n" ); document.write( "\n" ); document.write( "Thank you very much! I know I'm wrong becasue for 34 (g o f) I came out with an imaginary number.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #19840 by mukhopadhyay(490)\"\" \"About 
You can put this solution on YOUR website!
f(x)=x^2, g(x)=sqrt(x-3) ;
\n" ); document.write( "(f o g) = f(g(x)) = f(sqrt(x-3)) = (x-3); Domain: x >= 3;
\n" ); document.write( "(g o f) = g(f(x)) = g(x^2) = (x^2-3); Domain: x is a real number;
\n" ); document.write( "(f o f) = f(f(x)) = f(x^2) = x^4; Domain: x is a real number;
\n" ); document.write( "(g o g) = g(g(x)) = g(sqrt(x-3)) = Sqrt[sqrt(x-3)-3]; Domain: x>= 3
\n" ); document.write( ".........
\n" ); document.write( "f(x)=1/sqrt(x); g(x)=(x^2-4x)=x(x-4);
\n" ); document.write( "(f o g) = f(g(x)) = f(x^2-4x) = 1/[sqrt(x)(x-4)]; Domain: x < 0 or x>= 4;
\n" ); document.write( "(g o f) = g(f(x)) = g(1/sqrt(x)) = 1/x - 4/sqrt(x); Domain: x > 0 ;
\n" ); document.write( "(f o f) = f(f(x)) = f(1/sqrt(x)) = 1/[sqrt(1/sqrt(x))] = x^(1/4); Domain: x>0 ;
\n" ); document.write( "(g o g) = g(g(x)) = g(x^2-4x) = (x^2-4x)^2 - 4(x^2-4x) = (x^2-4x)(x^2-4x-4)
\n" ); document.write( "= x(x-4)(x^2-4x-4); Domain: x is a real number
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