Question

Solution set of the inequality $2-{\log }_2(x^3+3x)\ge 0$ is

• A. $[-4,1]$
• B. $[-4,-3)\cup (0,1]$
• C. $(-\infty ,-3)\cup (1,\infty )$
• D. $(-\infty ,-4)\cup [1,\infty )$

Answer 1

Answer: (B)

$[-4,-3)\cup (0,1]$

$2-{\log }_2(x^2+3x)\ge 0$

$2\ge {\log }_2(x^2+3x)$

$2^2\ge (x^2+3x)$

$(x^2+3x-4)\le 0$

$(x+4)(x-1)\le 0$

$xϵ[-4,1]$

And, $x^2+3x>0$

$x(x+3)>0$

$xϵ(-\infty ,-3)\bigcup (0,\infty )$

Taking intersection,

$xϵ[-4,-3)\bigcup (0,1]$