Find the domain of F(x)= v(3-vx)

Question

 Find the domain of F(x)= √(3-√x)

Answer 1

f(x) = √(3-√x)

 

We can't take square roots of negative numbers (if x is real) so x≥0 (so that √x is real) and 3-√x ≥ 0 (so that √(3-√x) is real).  

 

Thus, x ≥ 0 and -√x ≥ -3

 

        x ≥ 0 and √x ≤ 3

 

        x ≥ 0 and 0 ≤ x ≤ 9

 

Domain:  [0, 9]