what is the domain?

Question

what is the domain of (sqrt(?x)+?5)/ (x^2 -6x +8) in interval notation?

Answer 1

If only the x is under the square root sign, then the domain of this function will be all  non-negative values of x, except for where the denominator equals 0. That's because the domain of the square root of x is x greater than or equal to zero. Now, let's solve the denominator for x.

 

x² - 6x + 8 = 0

(x - 2)(x - 4) = 0

x = 2, 4

 

The domain is {[0, 2) , (2, 4) , (4, ∞)}