document.write( "Question 280605: How do you find the domain of (g o f)(x) for f(x)=x/x-2 and g(x)= 2x-4/x? \n" ); document.write( "

Algebra.Com's Answer #203996 by jsmallt9(3758) $\"\"$ $\"About$

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(Please put parentheses around numerators and denominators in the future.)

\n" ); document.write( "Assuming your functions are:
\n" ); document.write( " $\"f%28x%29+=+x%2F%28x-2%29\"$ and $\"g%28x%29+=+%282x-4%29%2Fx\"$ then
\n" ); document.write( "(g o f)(x) means g(f(x)). So
\n" ); document.write( "

\n" ); document.write( "The domain will be all Real numbers except those that make any of these denominators zero.

\n" ); document.write( "First let's look at the \"little\" denominators. They are both x-2. I hope it is clear that x=2 would make x-2 zero. (If not, then set x-2 = 0 and solve.) So we must exclude 2 from the domain.

\n" ); document.write( "The \"big\" denominator is $\"x%2F%28x-2%29\"$ . This is a fraction and if we understand fractions well we know that they are zero only if the numerator is zero. So x=0 would make $\"x%2F%28x-2%29\"$ equal to zero. (If this is not clear, then set $\"x%2F%28x-2%29+=+0\"$ and solve.) SO we must exclude x=0 from the domain, too.

\n" ); document.write( "So the domain of g(f(x)) is all Real numbers except 0 and 2. \n" ); document.write( "

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