document.write( "Question 349122: f(x)=1+(3/(x-2))
\n" ); document.write( "State the domain of f^-1(x) \n" ); document.write( "
Algebra.Com's Answer #249640 by nerdybill(7384)\"\" \"About 
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f(x)=1+(3/(x-2))
\n" ); document.write( "State the domain of f^-1(x)
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\n" ); document.write( "First, find the inverse of:
\n" ); document.write( "f(x)=1+(3/(x-2))
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\n" ); document.write( "Set f(x) to y:
\n" ); document.write( "y=1+(3/(x-2))
\n" ); document.write( "Switch x for y and y for x:
\n" ); document.write( "x=1+(3/(y-2))
\n" ); document.write( "Solve for y:
\n" ); document.write( "x(y-2)=(y-2)+3
\n" ); document.write( "xy-2x = y+1
\n" ); document.write( "-2x = y+1-xy
\n" ); document.write( "-2x-1 = y-xy
\n" ); document.write( "-2x-1 = y(1-x)
\n" ); document.write( "(-2x-1)/(1-x) = y
\n" ); document.write( "(2x+1)/(x-1) = y
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\n" ); document.write( "Therefore:
\n" ); document.write( "f^-1(x) = (2x+1)/(x-1)
\n" ); document.write( "Domain specifies values x can take --
\n" ); document.write( "All numbers except x=1 (denominator can't be zero)
\n" ); document.write( "OR, it can be specified as
\n" ); document.write( "(-oo, 1) U (1, oo)
\n" ); document.write( "where oo indicates infinity\r
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