Question 962475
If you mean
{{{f(x)=sqrt(9-4x^2)}}}
then the domain is wherever the function is defined. For the square root function, this is whenever the thing inside the square root is greater or equal to zero. Thus the input is valid when
{{{9-4x^2 ≥ 0 ⇔ 4x^2 ≤ 9 ⇔ x^2 ≤ 9/4 ⇔ |x| ≤ 9/4}}}
and the domain would be {x ∈ ℝ | -9/4 ≤ x ≤ 9/4}.
Here is the graph:
{{{graph(200, 200, -3, 3, -5, 5, sqrt(9-4x^2))}}}