$f (x) = l o g_{3} (5 - 4 x - x^{2})$ . Find range

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Solution

$(5 - 4 x - x^{2}) s h o u l d b e > 0$
$h e n c e x^{2} + 4 x - 5 < 0$
$(x + 5) (x - 1) < 0$
$x \in (- 5, 1)$
$t h e c u r v e 5 - 4 x - X^{2} w i l l b e m a x x = - 2 a n d m i n i m u m a t x = 1, 5$
$f (x) \in (- \infty, 2)$

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