Let f: R → R be defined as f(x) = 10 - x^2 , then:

The correct answer is Option (3) → f is neither one-one nor onto.

One-one: two different inputs give the same output,

    \(f(1) = 10 - 1 = 9\)
    \(f(-1) = 10 - 1 = 9\)

so f is not one-one.

Onto: since \(x^2 \ge 0\) for every real x,

    \(f(x) = 10 - x^2 \le 10\)

so a real number greater than 10, such as 11, is not an image of any x. The range is \((-\infty, 10]\), not all of R, so f is not onto.