CUET Preparation Today
Let $f: R→R$ be defined as $f(x) = 10x$. Then (Where R is the set of real numbers) |
f is both one-one and onto f is onto but not one-one f is one-one but not onto f is neither one-one nor onto |
f is both one-one and onto |
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 $\mathbb{R}$ |
