Relations & Functions
One-One and Onto Functions
Grade 12
Question:
<p>Set of values of \(a\) for which the function \(f : \mathbb{R} \to \mathbb{R}\), given by \(f(x) = x^3 + (a+2)x^2 + 3ax + 10\) is one-one is given by:</p>
<p>(a) \((-\infty, 1] \cup [4, \infty)\)</p>
<p>(b) \([1, 4]\)</p>
<p>(c) \([1, \infty)\)</p>
<p>(d) \([-\infty, 4]\)</p>
Step-by-Step Solution
Key Concept: A function is one-one if its derivative does not change sign or equals zero only at isolated points. Use \(f'(x) \geq 0\) or \(f'(x) \leq 0\) throughout the domain.
<p>Solution not provided in source text.</p>
Correct Answer: a