a) z^2 = [f(x,y)]^2 = 9 - 4x^2 - 4y^2

z^2 = 9 - 4 (x^2 + y^2)

If I understand the question correctly:

Note that x^2 + y^2 will be greater than or equal to zero, which makes -4 (x^2 + y^2) less than or equal to zero, which makes 9 - 4(x^2+y^2) less than or equal to 9.

If z^2 is less than or equal to 9, then z could be between -3 and 3.

Good luck!