Sets, Relations & Functions
General
Grade 11
Question:
Let f : (1,3) → R be a function defined by <span class="math-inline">f(x) = \frac{[x]}{1+x^2}</span>, where [x] denotes the greatest integer <span class="math-inline">\leq x</span>. Then the range of f is
\( \frac{2}{5} \)
\( \frac{3}{4} \)
\( \frac{2}{5} \)
\( \frac{3}{4} \)
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>log y=(log 5)(log x) → log x=log y/log 5 → x=10^{log y/log 5}=y^{1/log 5}.</p><div class="key-concept"><strong>Key Concept:</strong> Inverse via logarithm — base-10 log of both sides</div></div>
Correct Answer: 4