Find the domain of following functions f(x)= log_3(5-4x-x^2).

$f(x)= \log_3(5-4x-x^2)$

$= \log_3(9 - (x + 2)^2)$

f(x) is defined if $5 - 4x - x^2 > 0$

or $x^2+4x- 5 <0$

$⇒ (x- 1)(x+ 5)<0$

$⇒-5 <x<1$

So, domain is (-5, 1).