Find the domain of f. (Enter your answer using interval notation.) f(x) = 6x - 3 x2 - 9

Question

f(x)=

square root of 6x-3

all over x^2-9

Answer 1

f(x) = √(6x-3)/(x²-9)

 

The domain is the set of all values of x for which the function is defined.  

We can't take square roots of negative numbers and we can't divide by zero.  

 

So, 6x - 3 ≥ 0 and x² - 9 ≠ 0

 

Therefore, x ≥ 1/2 and x ≠ 3 or  -3

 

Domain:  [1/2, 3) ∪ (3, ∞)