Sets, Relations & Functions
General
Grade 11
Question:
<p>Let <span class="math-inline">\(f:\mathbb{N}\setminus\{1\}\to\mathbb{N}\)</span>, <span class="math-inline">\(f(n)=\)</span>highest prime factor of <span class="math-inline">\(n\)</span>. Determine nature of <span class="math-inline">\(f\)</span>.</p>
One-one and onto
Many-one onto
One-one into
<strong>Neither one-one nor onto</strong>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Not one-one: f(2)=f(4)=2. Not onto: range is primes only, not all of ℕ.</p><div class="key-concept"><strong>Key Concept:</strong> Range restricted to primes → not onto ℕ</div></div>
Correct Answer: Neither one-one nor onto