Question 102466
{{{f(x)=(3x+1)/(x^2+4)}}} Start with the given function



{{{x^2+4=0}}} Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.


{{{x^2=-4}}} Subtract 4 from both sides


{{{x=0+-sqrt(-4)}}} Take the square root of both sides


Since you cannot take the square root of a negative number and get a real number, the result will be imaginary



So that means there are no real numbers which will make the denominator equal to zero



So the domain is: 


x is the element of all real numbers