Question 104958
For the first function, 
{{{f(x)=sqrt(3x-4)}}}
the value inside the square root must always be greater than or equal to zero for the function to be defined. 
{{{3x-4>=0}}}
{{{3x>=4}}}
{{{x>=4/3}}} The domain for {{{f(x)=sqrt(3x-4)}}}
For the second function, 
{{{g(x) = (-2x+1) / (1-3x)}}}
you need to avoid any values that make the denominator zero since division by zero is undefined. 
{{{1-3x=0}}}
{{{1=3x}}}
{{{x=1/3}}} 
In this case, all values are acceptable except x=1/3. 
{{{x<1/3}}} and {{{x>1/3}}} is the domain for {{{g(x)= (-2x+1) / (1-3x)}}}