SOLUTION: for the function f (x)=sqrt2x-1, g(x)=1/x-3 find f/g and give the domain

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Question 1048528: for the function f (x)=sqrt2x-1, g(x)=1/x-3 find f/g and give the domain
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=sqrt%282x-1%29
+g%28x%29=1%2F%28x-3%29
find f%2Fg
f%2Fg=sqrt%282x-1%29%2F%281%2F%28x-3%29%29
f%2Fg=%28x-3%29sqrt%282x-1%29

and the domain is:
if %28x-3%29=0->highlight%28x=3%29; so,highlight%28x%3C3%29 or highlight%28x%3E3%29
to have a solution for sqrt%282x-1%29, %282x-1%29 cannot be equal to zero
if %282x-1%29=0->2x=1->highlight%28x=1%2F2%29;so, highlight%28x%3E1%2F2%29

so, exclude x=3 and highlight%28x=1%2F2%29 and domain is

{ x element R : 1%2F2%3C=x%3C3 or x%3E3 }

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28x-3%29sqrt%282x-1%29%29+