# SOLUTION: How do you find the domain of (g o f)(x) for f(x)=x/x-2 and g(x)= 2x-4/x?

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 Click here to see ALL problems on Rational-functions 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?Answer by jsmallt9(3296)   (Show Source): You can put this solution on YOUR website!(Please put parentheses around numerators and denominators in the future.) Assuming your functions are: and then (g o f)(x) means g(f(x)). So The domain will be all Real numbers except those that make any of these denominators zero. 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. The "big" denominator is . 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 equal to zero. (If this is not clear, then set and solve.) SO we must exclude x=0 from the domain, too. So the domain of g(f(x)) is all Real numbers except 0 and 2.