<p>Find the domain of <span class="math-inline">\(f(x)=\dfrac{1}{4-x^2}+\log_{10}(x^3-x)\)</span>.</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Need: 4-x²≠0 → x≠±2; and x³-x>0 → x(x-1)(x+1)>0 → x∈(-1,0)∪(1,∞). Exclude x=2: domain=(-1,0)∪(1,2)∪(2,∞).</p><div class="trap-box"><strong>Trap:</strong> Logarithm needs strict positivity.</div><div class="key-concept"><strong>Key Concept:</strong> Domain = intersection of domains of all component pieces</div></div>
Correct Answer: (-1,0)∪(1,2)∪(2,∞)