Sets, Relations & Functions
General
Grade None
Question:
For <span class="math-inline">x \in \left(0, \frac{3}{2}\right)</span>, let <span class="math-inline">f(x) = \sqrt{x}</span>, <span class="math-inline">g(x) = \tan x</span> and <span class="math-inline">h(x) = \frac{1 - x^2}{1 + x^2}</span>. If <span class="math-inline">f(x) = (hof)og(x)</span>, then <span class="math-inline">\(\phi \left( \frac{\pi}{3} \right)\)</span> is equal to :
\tan \frac{\pi}{12}
\tan \frac{7\pi}{12}
\tan \frac{11\pi}{12}
\tan \frac{5\pi}{12}
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>f(i)=3ⁱ. Sum=(3^{n+1}-3)/2=363 → 3^{n+1}=729=3⁶ → n=5.</p><div class="key-concept"><strong>Key Concept:</strong> Geometric sum formula</div></div>
Correct Answer: 3