Find the domain of the function

Question

g(x) =     √x

         _______
      4x² + 3x − 1

Answer 1

From the numerator, domain is  x≥0.

 

Now lets look at the denominator.  Set the denominator equal to zero.

 

4x² + 3x - 1 = 0

 

 

Solve for x from this equation.

 

(4x - 1)(x + 1) = 0

 

x = 1/4         and          x = -1

 

 

Using this as well as the domain from the numerator, domain is in the interval

 

[0, 1/4)∪(1/4, ∞)