Let $f: R→R$ 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
$f:\mathbb{R}\to \mathbb{R}$ is defined by $f(x)=10x$.
Domain of $f$ is $\mathbb{R}$ because every real $x$ is allowed.
Range of $f$ is also $\mathbb{R}$ because $10x$ covers all real values as $x$ varies over $\mathbb{R}$.
Thus $f$ is both one–one and onto.
Final answer: the domain is $\mathbb{R}$ and the range is $\mathbb{R}$