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

(-5, 1) (-5, 2) (5, -1) (-5, -1)

(-5, 1)

$f(x)= \log_3(5-4x-x^2)$ $= \log_3(9 - (x + 2)^2)$ 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).