Let \(f: \mathrm{R} \to \mathrm{R}\) be defined as \(f(x) = 10x\). Then (Where R is the set of real numbers)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → f is both one-one and onto
One-one: let \(f(x_1) = f(x_2)\) for real \(x_1, x_2\).
\(10x_1 = 10x_2\)
\(x_1 = x_2\)
So different inputs give different outputs.
Onto: let y be any real number. Then \(x = \frac{y}{10}\) is also real, and
\(\displaystyle f\left(\frac{y}{10}\right) = 10 \cdot \frac{y}{10} = y\)
So every real number is an image, the range is the whole of R, and f is both one-one and onto (a bijection).
NCERT (2026-27 edition):
Types of Functions
