The domain of the function f(x)

$f(x)=\sqrt{9-x}+\frac{1}{\sqrt{x^{2}-16}}$

here f(x) is defined for 9 − x ≥ 0

i.e 9 ≥ x

i.e x ≤ 9

and x2 − 16 > 0 

i.e x2 > 16 

i.e x > 4 or x < −4 

∴ f(x) is defined for common region is (−∞, −4) ∪ (4, 9]

∴ Domain of f(x) is  (−∞, −4) ∪ (4, 9]