Question

The domain of the function $f\left(x\right)=\sqrt{9-x}+\frac{1}{\sqrt{x^2-16}}$ is equal to __________ .

Answer 1

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