If \(f:[3, \infty) \rightarrow A\) defined by \(f(x)=x^2\) is an onto function, then A is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \([9, \infty)\)
A function is onto when its codomain equals its range. So A must be the range of \(f(x) = x^2\) on \([3, \infty)\).
For \(x \ge 3\), \(x^2\) is increasing:
\(f(3) = 9\)
\(f(x) \to \infty\) as \(x \to \infty\)
Every value \(y \ge 9\) is reached, at \(x = \sqrt{y} \ge 3\), and no value below 9 is reached. So the range is \([9, \infty)\), and \(A = [9, \infty)\).