Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>Range of <math>f(x) = \sin^{-1}\log_{[x]} + \log(\sin^{-1}[x])</math>, where <math>[]</math> denotes GIF is</p>
<p>(a) 1</p>
<p>(b) 2</p>
<p>(c) <math>\log 2</math></p>
<p>(d) <math>\log\frac{\pi}{2}</math></p>
Step-by-Step Solution
Key Concept: Determine the domain by analyzing the constraints of both terms, then evaluate the range on that domain.
<p><strong>Solution:</strong></p><p>Domain of <math>f(x)</math> is <math>[1, 2)</math>.</p><p>Range is <math>\left[0, \log\frac{\pi}{2}\right)</math></p>
Correct Answer: C