document.write( "Question 193570: Can you please help me with the following problem:\r
\n" ); document.write( "\n" ); document.write( "Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5)\r
\n" ); document.write( "\n" ); document.write( "I know that the domain of f(x) is (-infinity,2)U (2,infinity) and g(x) is (-infinity,5)U (5,infinity)
\n" ); document.write( "I know that f(x) has got to be set to the number that the domain cannot use in g(x)
\n" ); document.write( "So that would be 5=4/(x-2)
\n" ); document.write( "Then multiply each side by (x-2). (x-2)(5)=(4/(x-2))(x-2) this cancel out the denominator.\r
\n" ); document.write( "\n" ); document.write( "Then the problem would be 5x-10=4, subtract 10 from each side to isolate the variable. 5x-10+10=4+10 => 5x=14. Then to isolate x, x would have to be divided by 5. 5x/5=14/5 => x=14/5\r
\n" ); document.write( "\n" ); document.write( "So would the domain be (-infinity,2)U(2,(14/5))U((14/5),5)U(5,infinity)?\r
\n" ); document.write( "\n" ); document.write( "please let me know if any mistakes were made\r
\n" ); document.write( "\n" ); document.write( "thanks!
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #145289 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5)
\n" ); document.write( "f[g(x)] = f[3/(x-5)] = 5/[3/(x-5) -2] = 5/[(3-2x+10)/(x-5)]
\n" ); document.write( "= 5/[13-2x/(x-5)/
\n" ); document.write( "= [5(x-5)]/[13-2x]
\n" ); document.write( "-----------------------
\n" ); document.write( "Domain: All Real numbers except x = 13/2
\n" ); document.write( "==============================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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