10:I[6034,["878","static/chunks/9da6db1e-321469e27dc51aa4.js","954","static/chunks/d3ac728e-23c45ec216700eea.js","972","static/chunks/972-cf0c19383a04ee27.js","605","static/chunks/605-e6d88733e2ed50de.js","718","static/chunks/718-16004f17ca4d7da3.js","957","static/chunks/957-15c5f8c3ab68f8ee.js","34","static/chunks/34-c897dff191c58929.js","801","static/chunks/app/questions/%5Bslug%5D/page-d9aea32ec2d4c76b.js"],"default"] 11:I[8845,["878","static/chunks/9da6db1e-321469e27dc51aa4.js","954","static/chunks/d3ac728e-23c45ec216700eea.js","972","static/chunks/972-cf0c19383a04ee27.js","605","static/chunks/605-e6d88733e2ed50de.js","718","static/chunks/718-16004f17ca4d7da3.js","957","static/chunks/957-15c5f8c3ab68f8ee.js","34","static/chunks/34-c897dff191c58929.js","801","static/chunks/app/questions/%5Bslug%5D/page-d9aea32ec2d4c76b.js"],"default"] 12:T44c,We solve $|x^2 - 9| < |x + 3|$. Since $x^2 - 9 = (x-3)(x+3)$, we have $|x+3||x-3| < |x+3|$. If $x = -3$, $0 < 0$ is false. For $x \neq -3$, we can divide by $|x+3| > 0$ to get $|x-3| < 1$. This implies $-1 < x-3 < 1$, so $2 < x < 4$. Wait, checking the original expression: $f(x) < 0 \implies |(x-3)(x+3)| < |x+3|$. This is $|x-3| < 1$ AND $x \neq -3$. Thus $2 < x < 4$ is the solution for $x > -3$. What about $x < -3$? If $x < -3$, $|x+3| = -(x+3)$, so $|x-3|(-1) < -1$ is not right. Actually, $f(x) < 0 \implies |x^2-9| < |x+3|$. If $x < -3$, $x^2-9 > 0$, so $x^2-9 < -(x+3) \implies x^2+x-6 < 0 \implies (x+3)(x-2) < 0$. Since $x < -3$, this is never true. Thus, the only range is $(2, 4)$. Correction: Re-evaluating the sign, the interval is $(-4, -3) \cup (2, 4)$ is incorrect. Re-solve: $|x^2-9| < |x+3|$. Cases: 1) $x^2-9 = x+3 \implies x^2-x-12=0 \implies (x-4)(x+3)=0$. 2) $x^2-9 = -(x+3) \implies x^2+x-6=0 \implies (x+3)(x-2)=0$. Roots are $-3, 2, 4$. Testing intervals: $x=0 \to |-9| < |3| (F)$; $x=3.5 \to |3.25| < |6.5| (T)$; $x=-4 \to |7| < |1| (F)$. The correct interval is $(2, 4)$.5:["$","div",null,{"className":"min-h-screen bg-[#0f0f23]","children":[["$","script",null,

A function is defined as f(x)=∣x2−9∣−∣x+3∣f(x) = |x^2 - 9| - |x + 3|f(x)=∣x2−9∣−∣x+3∣. Determine all intervals of xxx such that f(x)<0f(x) < 0f(x)<0.

A function is defined as $f(x) = |x^2 - 9| - |x + 3|$ . Determine all intervals of $x$ such that $f(x) < 0$ .