Determine the domain of f(x). Give your answer using interval notation. F(x)= (x-7)/Sqr(11-4x).

Question

I am having trouble trying to factor the denominator in order to find the domain And putting it in interval form. 

Answer 1

x-7 is the equation of a line, so it's domain is all real numbers, (-∞,∞).  For √(11-4x), remember that you cannot take the square root of a negative number.  So we must have:

 

11 - 4x ≥ 0

 

Since we also cannot divide by 0, we cannot have 11 - 4x = 0 so we have to exclude the zero:

 

11 - 4x > 0

11 > 4x

11/4 > x

 

So the domain is limited by the denominator to x < 11/4, or (-∞,11/4)