Functions
General
Grade 12
Question:
Let f(x) = 2x - \left\lfloor \frac{x}{\pi} \right\rfloor and g(x) = \cos x, where \{ . \} denotes fractional part function, then period of gof(x) is -
\frac{\pi}{2}
\pi
\frac{3\pi}{2}
\frac{\pi}{4}
Step-by-Step Solution
<div class="solution"><p>y=(x+1)²+2 → x+1=±√(y-2). Since x≤-2, x+1≤-1<0 → negative root: x=-1-√(y-2).</p><p><span class="math-block">$$f^{-1}(x) = -\sqrt{x-2}-1$$</span></p><div class="trap-box"><strong>Trap:</strong> Positive root violates the restricted domain.</div><div class="key-concept"><strong>Key Concept:</strong> Inverse of restricted parabola — domain determines root sign</div></div>
Correct Answer: B